From 191af164b3c412b4bcdd5abdf53e9493af04f115 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:17:14 +0200 Subject: [PATCH 01/13] =?UTF-8?q?implicit=20type=20arguments=20for=20`asso?= =?UTF-8?q?ciative-=CE=A3`?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../functors-precategories.lagda.md | 9 +----- .../functors-set-magmoids.lagda.md | 8 +---- src/category-theory/groupoids.lagda.md | 15 +--------- .../replete-subprecategories.lagda.md | 2 +- ...ructure-equivalences-set-magmoids.lagda.md | 8 ++--- ...resentatives-equivalence-relation.lagda.md | 6 ++-- .../coherently-invertible-maps.lagda.md | 2 +- ...roduct-decompositions-subuniverse.lagda.md | 16 ++++------ .../decidable-equivalence-relations.lagda.md | 4 +-- .../decidable-propositions.lagda.md | 2 +- ...-theorem-of-equivalence-relations.lagda.md | 15 ++-------- src/foundation/invertible-maps.lagda.md | 18 +++-------- src/foundation/logical-equivalences.lagda.md | 4 +-- src/foundation/partitions.lagda.md | 5 +--- ...roduct-decompositions-subuniverse.lagda.md | 30 ++++++++----------- .../relaxed-sigma-decompositions.lagda.md | 14 ++++----- src/foundation/sigma-decompositions.lagda.md | 14 ++++----- src/foundation/split-idempotent-maps.lagda.md | 8 +---- .../structured-type-duality.lagda.md | 5 +--- ...rithmetic-cartesian-product-types.lagda.md | 12 ++++---- ...e-arithmetic-dependent-pair-types.lagda.md | 4 +-- ...zer-groups-concrete-group-actions.lagda.md | 5 +--- .../equality-of-pseudometric-spaces.lagda.md | 5 +--- ...y-of-metric-spaces-and-isometries.lagda.md | 11 +++---- ...metric-spaces-and-short-functions.lagda.md | 9 ++---- src/ring-theory/isomorphisms-rings.lagda.md | 11 ++----- src/set-theory/russells-paradox.lagda.md | 11 ++----- ...-species-of-types-in-subuniverses.lagda.md | 6 ++-- ...uchy-composition-species-of-types.lagda.md | 10 +++---- ...chy-exponentials-species-of-types.lagda.md | 2 +- ...-species-of-types-in-subuniverses.lagda.md | 6 ++-- ...-species-of-types-in-subuniverses.lagda.md | 2 +- ...let-exponentials-species-of-types.lagda.md | 2 +- ...-species-of-types-in-subuniverses.lagda.md | 6 ++-- ...-species-of-types-in-subuniverses.lagda.md | 6 ++-- src/structured-types/h-spaces.lagda.md | 2 +- .../descent-circle-subtypes.lagda.md | 21 ++----------- ...ttening-lemma-sequential-colimits.lagda.md | 6 ---- .../hatchers-acyclic-type.lagda.md | 6 +--- .../infinite-cyclic-types.lagda.md | 7 +---- ...erty-suspensions-of-pointed-types.lagda.md | 14 ++------- src/trees/directed-trees.lagda.md | 6 +--- src/trees/extensional-w-types.lagda.md | 5 +--- src/trees/functoriality-w-types.lagda.md | 9 ++---- .../binomial-types.lagda.md | 16 ++-------- .../cartesian-product-types.lagda.md | 2 +- .../counting-dependent-pair-types.lagda.md | 4 +-- .../decidable-equivalence-relations.lagda.md | 7 +---- .../dependent-pair-types.lagda.md | 4 +-- .../fibers-of-maps.lagda.md | 4 +-- .../inhabited-finite-types.lagda.md | 6 ++-- .../sums-of-natural-numbers.lagda.md | 2 +- .../type-duality.lagda.md | 11 +++---- 53 files changed, 123 insertions(+), 302 deletions(-) diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index 0a9c7a225e..d80d8fbe24 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -278,14 +278,7 @@ module _ equiv-ap-emb ( comp-emb ( emb-subtype (is-functor-prop-map-Precategory C D)) - ( emb-equiv - ( inv-associative-Σ - ( obj-Precategory C → obj-Precategory D) - ( λ F₀ → - { x y : obj-Precategory C} → - hom-Precategory C x y → - hom-Precategory D (F₀ x) (F₀ y)) - ( pr1 ∘ is-functor-prop-map-Precategory C D)))) + ( emb-equiv (inv-associative-Σ))) eq-map-eq-functor-Precategory : (F = G) → (map-functor-Precategory C D F = map-functor-Precategory C D G) diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index 63fbec6ca4..19c562a888 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -234,13 +234,7 @@ module _ ( emb-subtype ( preserves-comp-hom-prop-map-Set-Magmoid A B)) ( emb-equiv - ( inv-associative-Σ - ( obj-Set-Magmoid A → obj-Set-Magmoid B) - ( λ F₀ → - { x y : obj-Set-Magmoid A} → - hom-Set-Magmoid A x y → - hom-Set-Magmoid B (F₀ x) (F₀ y)) - ( preserves-comp-hom-map-Set-Magmoid A B)))) + ( inv-associative-Σ))) eq-map-eq-functor-Set-Magmoid : F = G → map-functor-Set-Magmoid A B F = map-functor-Set-Magmoid A B G diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index 2fb548ee06..57d4f11e78 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -151,20 +151,7 @@ module _ ( λ (y , p) → Σ ( Σ (y = x) (λ q → q ∙ p = refl)) ( λ (q , l) → p ∙ q = refl))) - ( ( equiv-tot - ( λ y → - equiv-tot - ( λ p → - associative-Σ - ( y = x) - ( λ q → q ∙ p = refl) - ( λ (q , r) → p ∙ q = refl)))) ∘e - ( associative-Σ - ( type-1-Type X) - ( λ y → x = y) - ( λ (y , p) → - Σ ( Σ (y = x) (λ q → q ∙ p = refl)) - ( λ (q , l) → p ∙ q = refl)))) + ( equiv-tot (λ y → equiv-tot (λ p → associative-Σ)) ∘e associative-Σ) ( is-contr-iterated-Σ 2 ( is-torsorial-Id x , ( x , refl) , diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 3de9094024..c98a58ff9f 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -247,7 +247,7 @@ module _ ( equiv-tot ( equiv-is-iso-is-iso-base-is-replete-Subprecategory C P is-replete-P {x} {y})) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot ( λ f → ( commutative-product) ∘e diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index 97006c2dcd..57c77791f0 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -122,15 +122,15 @@ module _ compute-structure-equiv-Set-Magmoid : componentwise-structure-equiv-Set-Magmoid ≃ structure-equiv-Set-Magmoid A B compute-structure-equiv-Set-Magmoid = - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot ( λ F₀ → - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e equiv-tot (λ _ → equiv-left-swap-Σ) ∘e ( equiv-left-swap-Σ) ∘e ( equiv-tot ( λ is-equiv-F₀ → - ( associative-Σ _ _ _) ∘e + ( associative-Σ) ∘e ( equiv-right-swap-Σ) ∘e ( equiv-Σ-equiv-base ( λ E₁' → @@ -138,7 +138,7 @@ module _ ( ( distributive-implicit-Π-Σ) ∘e ( equiv-implicit-Π-equiv-family ( λ _ → distributive-implicit-Π-Σ)))))))) ∘e - ( associative-Σ _ _ _) + ( associative-Σ) ``` ### Structure equivalences of set-magmoids characterize their equality diff --git a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md index 6ba3e69b75..0cf976d904 100644 --- a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md +++ b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md @@ -83,10 +83,8 @@ module _ fundamental-theorem-id ( is-contr-equiv ( Σ A (λ x → P x × sim-equivalence-relation R a x)) - ( ( associative-Σ A P (λ z → sim-equivalence-relation R a (pr1 z))) ∘e - ( equiv-tot - ( λ t → - is-effective-class R a (pr1 t)))) + ( ( associative-Σ) ∘e + ( equiv-tot (λ t → is-effective-class R a (pr1 t)))) ( H a)) ( λ y → ap (class-representatives H) {pair a p} {y}) diff --git a/src/foundation/coherently-invertible-maps.lagda.md b/src/foundation/coherently-invertible-maps.lagda.md index 03f1ed4655..5bdd4981a1 100644 --- a/src/foundation/coherently-invertible-maps.lagda.md +++ b/src/foundation/coherently-invertible-maps.lagda.md @@ -78,7 +78,7 @@ module _ is-proof-irrelevant-is-coherently-invertible H = is-contr-equiv' ( _) - ( associative-Σ _ _ _) + ( associative-Σ) ( is-contr-Σ ( is-contr-section-is-coherently-invertible H) ( section-is-coherently-invertible H) diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index 3d8495b9a1..290062c879 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -294,10 +294,7 @@ module _ binary-coproduct-Decomposition-subuniverse P X ≃ binary-coproduct-Decomposition-subuniverse P X equiv-commutative-binary-coproduct-Decomposition-subuniverse = - ( associative-Σ - ( type-subuniverse P) - ( λ _ → type-subuniverse P) - ( _)) ∘e + ( associative-Σ) ∘e ( ( equiv-Σ ( _) ( commutative-product) @@ -307,10 +304,7 @@ module _ ( inclusion-subuniverse P (pr1 x)) ( inclusion-subuniverse P (pr2 x))) (inclusion-subuniverse P X))) ∘e - ( ( inv-associative-Σ - ( type-subuniverse P) - ( λ _ → type-subuniverse P) - ( _)))) + ( ( inv-associative-Σ))) ``` ### Equivalence between iterated coproduct and ternary coproduct decomposition @@ -506,8 +500,8 @@ module _ ( eq-type-Prop (P _))) ( eq-is-prop is-property-is-empty))) ( ( raise-empty l1 , C1) , is-empty-raise-empty)) ∘e - ( ( inv-associative-Σ _ _ _) ∘e + ( ( inv-associative-Σ) ∘e ( ( equiv-tot (λ _ → commutative-product)) ∘e - ( ( associative-Σ _ _ _))))))) ∘e - ( ( associative-Σ _ _ _)) + ( ( associative-Σ))))))) ∘e + ( ( associative-Σ)) ``` diff --git a/src/foundation/decidable-equivalence-relations.lagda.md b/src/foundation/decidable-equivalence-relations.lagda.md index 7616e35b46..809ae075f3 100644 --- a/src/foundation/decidable-equivalence-relations.lagda.md +++ b/src/foundation/decidable-equivalence-relations.lagda.md @@ -513,8 +513,8 @@ equiv-Surjection-Into-Set-Decidable-Equivalence-Relation {l1} A = ( is-set-has-decidable-equality)) ∘e ( commutative-product)) ∘e ( equiv-left-swap-Σ)))) ∘e - ( associative-Σ _ _ _) ∘e - ( associative-Σ _ _ _) ∘e + ( associative-Σ) ∘e + ( associative-Σ) ∘e ( equiv-type-subtype ( λ surj → is-prop-Π diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index 8215e2af78..6bd0b0b964 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -77,7 +77,7 @@ split-Decidable-Prop : ((Σ (Prop l) type-Prop) + (Σ (Prop l) (λ Q → ¬ (type-Prop Q)))) split-Decidable-Prop {l} = ( left-distributive-Σ-coproduct (Prop l) (λ Q → pr1 Q) (λ Q → ¬ (pr1 Q))) ∘e - ( inv-associative-Σ (UU l) is-prop (λ X → is-decidable (pr1 X))) + ( inv-associative-Σ) ``` ### The type of decidable propositions in universe level `l` is equivalent to the type of booleans diff --git a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md index 8bd7600e74..3505a0eb28 100644 --- a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md +++ b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md @@ -118,10 +118,7 @@ module _ ( Σ ( Σ ( block-partition P) ( λ B → is-in-block-partition P B x)) ( λ B → is-in-block-partition P (pr1 B) y)) - ( associative-Σ - ( block-partition P) - ( λ U → is-in-block-partition P U x) - ( λ U → is-in-block-partition P (pr1 U) y)) + ( associative-Σ) ( is-contr-Σ ( is-contr-block-containing-element-partition P x) ( Q , p) @@ -291,10 +288,7 @@ module _ ( ( left-unit-law-Σ-is-contr ( is-contr-block-containing-element-partition P a) ( center-block-containing-element-partition P a)) ∘e - ( inv-associative-Σ - ( block-partition P) - ( λ B → is-in-block-partition P B a) - ( λ B → is-in-block-partition P (pr1 B) x)))) ∘iff + ( inv-associative-Σ))) ∘iff ( K x)))) ( is-block-class-partition P a)) @@ -322,10 +316,7 @@ module _ ( is-contr-block-containing-element-partition P a) ( ( make-block-partition P Q H) , ( make-is-in-block-partition P Q H a q))) ∘e - ( inv-associative-Σ - ( block-partition P) - ( λ B → is-in-block-partition P B a) - ( λ B → is-in-block-partition P (pr1 B) x)))) ∘e + ( inv-associative-Σ))) ∘e ( compute-is-in-block-partition P Q H x))))) has-same-elements-partition-equivalence-relation-partition : diff --git a/src/foundation/invertible-maps.lagda.md b/src/foundation/invertible-maps.lagda.md index 47fb7cca31..fbd683270d 100644 --- a/src/foundation/invertible-maps.lagda.md +++ b/src/foundation/invertible-maps.lagda.md @@ -255,10 +255,7 @@ pr2 (pr2 (is-invertible-id-htpy-id-id A H)) = H triangle-is-invertible-id-htpy-id-id : {l : Level} (A : UU l) → ( is-invertible-id-htpy-id-id A) ~ - ( ( map-associative-Σ - ( A → A) - ( λ g → (id ∘ g) ~ id) - ( λ s → (pr1 s ∘ id) ~ id)) ∘ + ( ( map-associative-Σ) ∘ ( map-inv-left-unit-law-Σ-is-contr { B = λ s → (pr1 s ∘ id) ~ id} ( is-contr-section-is-equiv (is-equiv-id {_} {A})) @@ -271,10 +268,7 @@ abstract is-equiv-is-invertible-id-htpy-id-id A = is-equiv-left-map-triangle ( is-invertible-id-htpy-id-id A) - ( map-associative-Σ - ( A → A) - ( λ g → (id ∘ g) ~ id) - ( λ s → (pr1 s ∘ id) ~ id)) + ( map-associative-Σ) ( map-inv-left-unit-law-Σ-is-contr ( is-contr-section-is-equiv is-equiv-id) ( pair id refl-htpy)) @@ -282,7 +276,7 @@ abstract ( is-equiv-map-inv-left-unit-law-Σ-is-contr ( is-contr-section-is-equiv is-equiv-id) ( pair id refl-htpy)) - ( is-equiv-map-associative-Σ _ _ _) + ( is-equiv-map-associative-Σ) ``` ### The type of invertible maps is equivalent to the type of free loops on equivalences @@ -336,11 +330,7 @@ module _ equiv-is-retraction-section-is-invertible : (f : A → B) → Σ (section f) (λ g → (map-section f g) ∘ f ~ id) ≃ is-invertible f - equiv-is-retraction-section-is-invertible f = - associative-Σ - ( B → A) - ( λ g → f ∘ g ~ id) - ( λ g → (map-section f g) ∘ f ~ id) + equiv-is-retraction-section-is-invertible f = associative-Σ equiv-free-loop-equivalence-invertible-equivalence : free-loop (A ≃ B) ≃ Σ (A ≃ B) (is-invertible ∘ map-equiv) diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index d806e1ca3d..8be286d75e 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -234,9 +234,9 @@ compute-fiber-iff-equiv : compute-fiber-iff-equiv {A = A} {B} (f , g) = ( equiv-tot (λ _ → equiv-funext)) ∘e ( left-unit-law-Σ-is-contr (is-torsorial-Id' f) (f , refl)) ∘e - ( inv-associative-Σ (A → B) (_= f) _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ _ → equiv-left-swap-Σ)) ∘e - ( associative-Σ (A → B) _ _) ∘e + ( associative-Σ) ∘e ( equiv-tot (λ e → equiv-pair-eq (iff-equiv e) (f , g))) ``` diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index 11658b834b..a4076473e8 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -651,10 +651,7 @@ module _ ( refl)))) ∘e ( equiv-right-swap-Σ)) ∘e ( equiv-tot (λ ie → pr2 ie a)))) ∘e - ( associative-Σ - ( inhabited-subtype l2 A) - ( is-block-partition-Set-Indexed-Σ-Decomposition) - ( λ B → is-in-inhabited-subtype (pr1 B) a))) + ( associative-Σ)) ( is-torsorial-has-same-elements-inhabited-subtype ( pair ( λ x → diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index 8b340ce9dd..56db0b71c8 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -165,21 +165,15 @@ module _ binary-product-Decomposition-Subuniverse P X ≃ binary-product-Decomposition-Subuniverse P X equiv-commutative-binary-product-Decomposition-Subuniverse = - ( ( associative-Σ - ( type-subuniverse P) - ( λ _ → type-subuniverse P) - ( _)) ∘e - ( ( equiv-Σ - ( _) - ( commutative-product) - ( λ x → - equiv-postcomp-equiv - ( commutative-product) - (inclusion-subuniverse P X))) ∘e - ( ( inv-associative-Σ - ( type-subuniverse P) - ( λ _ → type-subuniverse P) - ( _))))) + ( associative-Σ) ∘e + ( ( equiv-Σ + ( _) + ( commutative-product) + ( λ x → + equiv-postcomp-equiv + ( commutative-product) + ( inclusion-subuniverse P X))) ∘e + ( inv-associative-Σ)) ``` ### Equivalence between iterated product and ternary product decomposition @@ -380,8 +374,8 @@ module _ ( eq-is-prop is-property-is-contr))) ( ( raise-unit l1 , C1) , is-contr-raise-unit)) ∘e - ( ( inv-associative-Σ _ _ _) ∘e + ( ( inv-associative-Σ) ∘e ( ( equiv-tot (λ _ → commutative-product)) ∘e - ( ( associative-Σ _ _ _)))))))) ∘e - ( ( associative-Σ _ _ _))) + ( ( associative-Σ)))))))) ∘e + ( ( associative-Σ))) ``` diff --git a/src/foundation/relaxed-sigma-decompositions.lagda.md b/src/foundation/relaxed-sigma-decompositions.lagda.md index 521c531132..7343b8bffc 100644 --- a/src/foundation/relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/relaxed-sigma-decompositions.lagda.md @@ -615,7 +615,7 @@ module _ ≃ Σ ( Σ U V) (λ uv → Y ((map-inv-equiv f) uv)) by inv-equiv ( equiv-Σ-equiv-base Y (inv-equiv f)) ≃ Σ U ( λ u → Σ (V u) (λ v → Y (map-inv-equiv f (u , v)))) - by associative-Σ U V (λ uv → Y (map-inv-equiv f uv)) + by associative-Σ map-displayed-fibered-Relaxed-Σ-Decomposition : displayed-Relaxed-Σ-Decomposition l4 (l3 ⊔ l5) l5 l3 A @@ -648,12 +648,10 @@ module _ matching-correspondence-inv-displayed-fibered-Relaxed-Σ-Decomposition = equivalence-reasoning A ≃ Σ M N by s - ≃ Σ M (λ m → Σ (P m) (Q m)) by equiv-Σ (λ m → Σ (P m) (Q m)) id-equiv t + ≃ Σ M (λ m → Σ (P m) (Q m)) + by equiv-Σ (λ m → Σ (P m) (Q m)) id-equiv t ≃ Σ (Σ M P) (λ (m , p) → Q m p) by inv-associative-Σ - ( M) - ( λ z → P z) - ( λ z → Q (pr1 z) (pr2 z)) map-inv-displayed-fibered-Relaxed-Σ-Decomposition : fibered-Relaxed-Σ-Decomposition (l2 ⊔ l4) l5 l2 l4 A @@ -748,14 +746,14 @@ module _ ( ap ( λ f → map-equiv (equiv-tot (inv-equiv ∘ t)) f) ( map-inv-eq-transpose-equiv - ( associative-Σ M P Y) + ( associative-Σ) ( inv ( map-eq-transpose-equiv ( equiv-Σ-equiv-base Y (inv-equiv id-equiv)) ( inv ( map-eq-transpose-equiv - ( associative-Σ M P Y) - ( is-section-map-inv-associative-Σ M P Y + ( associative-Σ) + ( is-section-map-inv-associative-Σ ( map-equiv (equiv-tot t ∘e s) x)))))))) ∙ ( inv ( preserves-comp-tot diff --git a/src/foundation/sigma-decompositions.lagda.md b/src/foundation/sigma-decompositions.lagda.md index 720de58abb..801d549a53 100644 --- a/src/foundation/sigma-decompositions.lagda.md +++ b/src/foundation/sigma-decompositions.lagda.md @@ -785,7 +785,7 @@ module _ ≃ Σ ( Σ U V) (λ uv → Y ((map-inv-equiv f) uv)) by inv-equiv ( equiv-Σ-equiv-base Y (inv-equiv f)) ≃ Σ U ( λ u → Σ (V u) (λ v → Y (map-inv-equiv f (u , v)))) - by associative-Σ U V (λ uv → Y (map-inv-equiv f uv)) + by associative-Σ map-displayed-fibered-Σ-Decomposition : displayed-Σ-Decomposition l4 (l3 ⊔ l5) l5 l3 A @@ -822,12 +822,10 @@ module _ matching-correspondence-inv-displayed-fibered-Σ-Decomposition = equivalence-reasoning A ≃ Σ M N by s - ≃ Σ M (λ m → Σ (P m) (Q m)) by equiv-Σ (λ m → Σ (P m) (Q m)) id-equiv t + ≃ Σ M (λ m → Σ (P m) (Q m)) + by equiv-Σ (λ m → Σ (P m) (Q m)) id-equiv t ≃ Σ (Σ M P) (λ (m , p) → Q m p) by inv-associative-Σ - ( M) - ( λ z → P z) - ( λ z → Q (pr1 z) (pr2 z)) map-inv-displayed-fibered-Σ-Decomposition : fibered-Σ-Decomposition (l2 ⊔ l4) l5 l2 l4 A @@ -929,14 +927,14 @@ module _ ( ap ( λ f → map-equiv (equiv-tot (inv-equiv ∘ t)) f) ( map-inv-eq-transpose-equiv - ( associative-Σ M P Y) + ( associative-Σ) ( inv ( map-eq-transpose-equiv ( equiv-Σ-equiv-base Y (inv-equiv id-equiv)) ( inv ( map-eq-transpose-equiv - ( associative-Σ M P Y) - ( is-section-map-inv-associative-Σ M P Y + ( associative-Σ) + ( is-section-map-inv-associative-Σ ( map-equiv (equiv-tot t ∘e s) x)))))))) ∙ ( inv ( preserves-comp-tot diff --git a/src/foundation/split-idempotent-maps.lagda.md b/src/foundation/split-idempotent-maps.lagda.md index 6935652587..502ec4df31 100644 --- a/src/foundation/split-idempotent-maps.lagda.md +++ b/src/foundation/split-idempotent-maps.lagda.md @@ -344,13 +344,7 @@ module _ Σ ( B retract-of A) ( λ (i , r , R) → i ∘ r ~ f))) ≃ Σ (A → A) (λ f → (Σ (retracts l2 A) (λ (B , i , r , R) → i ∘ r ~ f))) - by - equiv-tot - ( λ f → - inv-associative-Σ - ( UU l2) - ( _retract-of A) - ( λ (B , i , r , R) → i ∘ r ~ f)) + by equiv-tot (λ f → inv-associative-Σ) ≃ Σ (retracts l2 A) (λ (B , i , r , R) → Σ (A → A) (λ f → i ∘ r ~ f)) by equiv-left-swap-Σ ≃ retracts l2 A diff --git a/src/foundation/structured-type-duality.lagda.md b/src/foundation/structured-type-duality.lagda.md index cdbbcfc227..aeed20d718 100644 --- a/src/foundation/structured-type-duality.lagda.md +++ b/src/foundation/structured-type-duality.lagda.md @@ -43,10 +43,7 @@ equiv-Fiber-structure {l1} {l3} l P B = ( λ C → (b : B) → P (C b)) ( equiv-Fiber l B) ( λ f → equiv-Π-equiv-family (λ b → id-equiv)))) ∘e - ( inv-associative-Σ - ( UU (l1 ⊔ l)) - ( λ A → A → B) - ( λ f → structure-map P (pr2 f))) + ( inv-associative-Σ) ``` ```agda diff --git a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md index a4461efe4c..80593c1a75 100644 --- a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md +++ b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md @@ -73,27 +73,27 @@ module _ where map-associative-product : (A × B) × C → A × (B × C) - map-associative-product = map-associative-Σ A (λ _ → B) (λ _ → C) + map-associative-product = map-associative-Σ map-inv-associative-product : A × (B × C) → (A × B) × C - map-inv-associative-product = map-inv-associative-Σ A (λ _ → B) (λ _ → C) + map-inv-associative-product = map-inv-associative-Σ is-section-map-inv-associative-product : (map-associative-product ∘ map-inv-associative-product) ~ id is-section-map-inv-associative-product = - is-section-map-inv-associative-Σ A (λ _ → B) (λ _ → C) + is-section-map-inv-associative-Σ is-retraction-map-inv-associative-product : (map-inv-associative-product ∘ map-associative-product) ~ id is-retraction-map-inv-associative-product = - is-retraction-map-inv-associative-Σ A (λ _ → B) (λ _ → C) + is-retraction-map-inv-associative-Σ is-equiv-map-associative-product : is-equiv map-associative-product is-equiv-map-associative-product = - is-equiv-map-associative-Σ A (λ _ → B) (λ _ → C) + is-equiv-map-associative-Σ associative-product : ((A × B) × C) ≃ (A × (B × C)) - associative-product = associative-Σ A (λ _ → B) (λ _ → C) + associative-product = associative-Σ ``` ### The unit laws of cartesian product types with respect to contractible types diff --git a/src/foundation/type-arithmetic-dependent-pair-types.lagda.md b/src/foundation/type-arithmetic-dependent-pair-types.lagda.md index 022b2dc3a8..e89767d320 100644 --- a/src/foundation/type-arithmetic-dependent-pair-types.lagda.md +++ b/src/foundation/type-arithmetic-dependent-pair-types.lagda.md @@ -168,7 +168,7 @@ formalize both ways. ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : A → UU l2) (C : Σ A B → UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : A → UU l2} {C : Σ A B → UU l3} where map-associative-Σ : Σ (Σ A B) C → Σ A (λ x → Σ (B x) (λ y → C (x , y))) @@ -410,7 +410,7 @@ right-distributive-product-Σ : {l1 l2 l3 : Level} {A : UU l1} {B : A → UU l2} {C : UU l3} → ((Σ A B) × C) ≃ Σ A (λ a → B a × C) right-distributive-product-Σ {A} = - associative-Σ _ _ _ + associative-Σ ``` ## See also diff --git a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md index fccff9b2a3..52163be19a 100644 --- a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md +++ b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md @@ -55,10 +55,7 @@ module _ ( action-stabilizer-action-Concrete-Group x) is-transitive-action-stabilizer-action-Concrete-Group x = is-0-connected-equiv' - ( associative-Σ - ( classifying-type-Concrete-Group G) - ( type-Set ∘ X) - ( mere-eq (shape-Concrete-Group G , x))) + ( associative-Σ) ( is-0-connected-mere-eq ( ( shape-Concrete-Group G , x) , ( refl-mere-eq (shape-Concrete-Group G , x))) diff --git a/src/metric-spaces/equality-of-pseudometric-spaces.lagda.md b/src/metric-spaces/equality-of-pseudometric-spaces.lagda.md index e92824c132..5be6a0ba7f 100644 --- a/src/metric-spaces/equality-of-pseudometric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-pseudometric-spaces.lagda.md @@ -211,10 +211,7 @@ module _ equiv-tot ( λ e → equiv-eq (ap (is-isometry-Pseudometric-Space A B) refl)))) ∘e - ( associative-Σ - ( type-function-Pseudometric-Space A B) - ( is-equiv) - ( is-isometry-Pseudometric-Space A B ∘ map-equiv)) + ( associative-Σ) ``` ### Isometric equivalences between pseudometric spaces characterize their equality diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index a57d55d1a2..ba315c5ba8 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -110,12 +110,9 @@ module _ iso-Precategory precategory-isometry-Metric-Space A B ≃ isometric-equiv-Metric-Space' A B equiv-iso-isometric-equiv-Metric-Space' = - equiv-tot (λ f → commutative-product) ∘e - associative-Σ - ( type-function-Metric-Space A B) - ( is-isometry-Metric-Space A B) - ( is-equiv ∘ map-isometry-Metric-Space A B) ∘e - equiv-tot + ( equiv-tot (λ f → commutative-product)) ∘e + ( associative-Σ) ∘e + ( equiv-tot ( λ f → equiv-iff ( is-iso-prop-Precategory @@ -126,7 +123,7 @@ module _ ( is-equiv-Prop ( map-isometry-Metric-Space A B f)) ( is-equiv-is-iso-isometry-Metric-Space A B f) - ( is-iso-is-equiv-isometry-Metric-Space A B f)) + ( is-iso-is-equiv-isometry-Metric-Space A B f))) ``` ## See also diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index af0a7e0b14..564a2b9385 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -236,12 +236,9 @@ module _ iso-Precategory precategory-short-function-Metric-Space A B ≃ isometric-equiv-Metric-Space' A B equiv-isometric-equiv-iso-short-function-Metric-Space' = - equiv-tot - ( equiv-is-isometric-equiv-is-iso-short-function-Metric-Space A B) ∘e - associative-Σ - ( type-function-Metric-Space A B) - ( is-short-function-Metric-Space A B) - ( is-iso-Precategory precategory-short-function-Metric-Space {A} {B}) + ( equiv-tot + ( equiv-is-isometric-equiv-is-iso-short-function-Metric-Space A B)) ∘e + ( associative-Σ) ``` ## See also diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 5a982e30d8..31caeafe92 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -446,16 +446,9 @@ module _ equiv-iso-ab-iso-Ring : iso-Ring R S ≃ iso-ab-Ring equiv-iso-ab-iso-Ring = - ( inv-equiv - ( associative-Σ - ( hom-Ab (ab-Ring R) (ab-Ring S)) - ( is-iso-Ab (ab-Ring R) (ab-Ring S)) - ( λ f → is-ring-homomorphism-hom-Ab R S (pr1 f)))) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ f → commutative-product)) ∘e - ( associative-Σ - ( hom-Ab (ab-Ring R) (ab-Ring S)) - ( is-ring-homomorphism-hom-Ab R S) - ( λ f → is-iso-Ab (ab-Ring R) (ab-Ring S) (pr1 f))) ∘e + ( associative-Σ) ∘e ( equiv-type-subtype ( is-prop-is-iso-Ring R S) ( λ f → is-prop-is-iso-Ab (ab-Ring R) (ab-Ring S) (hom-ab-hom-Ring R S f)) diff --git a/src/set-theory/russells-paradox.lagda.md b/src/set-theory/russells-paradox.lagda.md index 9ca07432a8..40800d3405 100644 --- a/src/set-theory/russells-paradox.lagda.md +++ b/src/set-theory/russells-paradox.lagda.md @@ -134,7 +134,7 @@ paradox-Russell {l} H = { B = λ t → (pr1 t) ∉-𝕍 (pr1 t)} ( is-torsorial-Id' R') ( pair R' refl)) ∘e - ( ( inv-associative-Σ (𝕍 l) (_= R') (λ t → (pr1 t) ∉-𝕍 (pr1 t))) ∘e + ( ( inv-associative-Σ) ∘e ( ( equiv-tot ( λ t → ( commutative-product) ∘e @@ -146,14 +146,7 @@ paradox-Russell {l} H = ( eq-resize-𝕍 ( is-small-multiset-𝕍 is-small-lsuc t) ( is-small-R'))))))) ∘e - ( associative-Σ - ( 𝕍 l) - ( λ t → t ∉-𝕍 t) - ( λ t → - ( resize-𝕍 - ( pr1 t) - ( is-small-multiset-𝕍 is-small-lsuc (pr1 t))) = - ( R)))))) + ( associative-Σ)))) ``` ### There can be no surjective map `f : A → 𝒰` for any `A : 𝒰` diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index 0f5ad3fad1..4942733a8c 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -146,8 +146,8 @@ module _ ( equiv-product-right inv-distributive-Π-Σ) ∘e ( inv-equiv right-distributive-product-Σ) ∘e ( equiv-tot (λ _ → inv-equiv left-distributive-product-Σ)) ∘e - ( associative-Σ _ _ _))) ∘e - ( associative-Σ _ _ _) ∘e + ( associative-Σ))) ∘e + ( associative-Σ) ∘e ( equiv-Σ-equiv-base ( _) ( ( equiv-remove-redundant-prop @@ -166,7 +166,7 @@ module _ ( commutative-product) ∘e ( equiv-tot ( λ p → equiv-total-is-in-subuniverse-Σ-Decomposition P (X , p))))) ∘e - ( inv-associative-Σ _ _ _) + ( inv-associative-Σ) ``` ### Unit laws for Cauchy composition of species-subuniverse diff --git a/src/species/cauchy-composition-species-of-types.lagda.md b/src/species/cauchy-composition-species-of-types.lagda.md index 7e66fba693..7f52298c4e 100644 --- a/src/species/cauchy-composition-species-of-types.lagda.md +++ b/src/species/cauchy-composition-species-of-types.lagda.md @@ -78,7 +78,7 @@ left-unit-law-cauchy-composition-species-types {l1} F A = ( is-contr-type-trivial-Relaxed-Σ-Decomposition) ( trivial-Relaxed-Σ-Decomposition l1 A , is-trivial-trivial-Relaxed-Σ-Decomposition {l1} {l1} {A})) ∘e - ( ( inv-associative-Σ _ _ _) ∘e + ( ( inv-associative-Σ) ∘e ( ( equiv-tot ( λ D → equiv-tot (λ C → left-unit-law-Π-is-contr C (center C)))))) @@ -91,7 +91,7 @@ right-unit-law-cauchy-composition-species-types {l1} F A = ( is-contr-type-discrete-Relaxed-Σ-Decomposition) ( ( discrete-Relaxed-Σ-Decomposition l1 A) , is-discrete-discrete-Relaxed-Σ-Decomposition)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ _ → commutative-product)) ``` @@ -121,7 +121,7 @@ module _ ( inv-equiv right-distributive-product-Σ) ∘e ( equiv-tot ( λ D2 → - ( inv-associative-Σ _ _ _))) ∘e + ( inv-associative-Σ))) ∘e ( equiv-tot ( λ D2 → ( equiv-product-right @@ -134,10 +134,10 @@ module _ ( λ x → U (cotype-Relaxed-Σ-Decomposition D1 x)))) ∘e ( equiv-ind-Σ))) ∘e ( distributive-Π-Σ))))))) ∘e - ( associative-Σ _ _ _) ∘e + ( associative-Σ) ∘e ( equiv-Σ-equiv-base _ ( inv-equiv equiv-displayed-fibered-Relaxed-Σ-Decomposition)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot ( λ D → left-distributive-product-Σ ∘e equiv-product-right distributive-Π-Σ)) diff --git a/src/species/cauchy-exponentials-species-of-types.lagda.md b/src/species/cauchy-exponentials-species-of-types.lagda.md index 8ef9626dde..eafbf24565 100644 --- a/src/species/cauchy-exponentials-species-of-types.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types.lagda.md @@ -121,7 +121,7 @@ module _ ( compute-right-equiv-binary-coproduct-Decomposition-Σ-Decomposition ( D) ( b')))))))) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ d → distributive-Π-coproduct-binary-coproduct-Decomposition)) where reassociate : diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index 7f48882226..487ad89689 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -173,7 +173,7 @@ module _ ( equiv-ternary-left-iterated-coproduct-Decomposition-subuniverse P X C2)) ( λ d → associative-product _ _ _)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ d → right-distributive-product-Σ)) equiv-right-iterated-cauchy-product-species-subuniverse : @@ -200,7 +200,7 @@ module _ ( _) ( equiv-ternary-right-iterated-coproduct-Decomposition-subuniverse P X C2)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ d → left-distributive-product-Σ)) equiv-associative-cauchy-product-species-subuniverse : @@ -324,7 +324,7 @@ module _ P X C2)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ _ → commutative-product)) equiv-left-unit-law-cauchy-product-species-subuniverse : diff --git a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md index 1e6f11e40a..4617313292 100644 --- a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -63,7 +63,7 @@ module _ cauchy-series-species-subuniverse ≃ cauchy-series-species-types (Σ-extension-species-subuniverse P Q S) X equiv-cauchy-series-Σ-extension-species-subuniverse = - (equiv-tot (λ U → inv-associative-Σ _ _ _)) ∘e (associative-Σ _ _ _) + (equiv-tot (λ U → inv-associative-Σ)) ∘e (associative-Σ) ``` ### Equivalences diff --git a/src/species/dirichlet-exponentials-species-of-types.lagda.md b/src/species/dirichlet-exponentials-species-of-types.lagda.md index 8fdc9897a6..dccfe72288 100644 --- a/src/species/dirichlet-exponentials-species-of-types.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types.lagda.md @@ -99,7 +99,7 @@ module _ ( compute-right-equiv-binary-product-Decomposition-Π-Decomposition ( D) ( b')))))))) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ d → distributive-Π-coproduct-binary-coproduct-Decomposition)) where reassociate : diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index 1a872f00c7..89560cf1ab 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -194,7 +194,7 @@ module _ X C2) ( λ d → associative-product _ _ _)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ d → right-distributive-product-Σ)) equiv-right-iterated-dirichlet-product-species-subuniverse : @@ -232,7 +232,7 @@ module _ P X C2)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( ( equiv-tot (λ d → left-distributive-product-Σ))) equiv-associative-dirichlet-product-species-subuniverse : @@ -357,7 +357,7 @@ module _ P X C2)) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ _ → commutative-product)) equiv-left-unit-law-dirichlet-product-species-subuniverse : diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 0988bc7cc7..09bdc28548 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -118,8 +118,8 @@ module _ ( equiv-product-right inv-distributive-Π-Σ) ∘e ( inv-equiv right-distributive-product-Σ) ∘e ( equiv-tot (λ _ → inv-equiv left-distributive-product-Σ)) ∘e - ( associative-Σ _ _ _))) ∘e - ( associative-Σ _ _ _) ∘e + ( associative-Σ))) ∘e + ( associative-Σ) ∘e ( equiv-Σ-equiv-base ( _) ( ( equiv-remove-redundant-prop @@ -138,7 +138,7 @@ module _ ( commutative-product) ∘e ( equiv-tot ( λ p → equiv-total-is-in-subuniverse-Σ-Decomposition P (X , p))))) ∘e - ( inv-associative-Σ _ _ _) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ p → inv-equiv (equiv-is-small (C1 S T (X , p))))) ``` diff --git a/src/structured-types/h-spaces.lagda.md b/src/structured-types/h-spaces.lagda.md index be217b8539..156a5f15c5 100644 --- a/src/structured-types/h-spaces.lagda.md +++ b/src/structured-types/h-spaces.lagda.md @@ -194,5 +194,5 @@ module _ ( equiv-funext) ( λ _ → equiv-tot (λ _ → inv-equiv (equiv-right-whisker-concat refl))))) ∘e - ( associative-Σ _ _ _) + ( associative-Σ) ``` diff --git a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md index 8b2ed00fc2..b08f68dd4c 100644 --- a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md @@ -91,20 +91,7 @@ module _ ( B)) ( x , r) = ( x , r))) - by - associative-Σ - ( type-family-with-descent-data-circle A) - ( type-double-family-with-dependent-descent-data-circle A B) - ( λ u → - map-Σ - ( type-double-family-with-dependent-descent-data-circle A B) - ( map-aut-family-with-descent-data-circle A) - ( λ x → - map-dependent-automorphism-double-family-with-dependent-descent-data-circle - ( A) - ( B)) - ( u) = - u) + by associative-Σ ≃ Σ ( type-family-with-descent-data-circle A) ( λ x → ( is-in-subtype subtype-descent-data-circle-subtype x) × @@ -126,11 +113,7 @@ module _ ≃ Σ ( fixpoint-descent-data-circle ( descent-data-family-with-descent-data-circle A)) ( λ x → is-in-subtype subtype-descent-data-circle-subtype (pr1 x)) - by - inv-associative-Σ - ( type-family-with-descent-data-circle A) - ( λ x → map-aut-family-with-descent-data-circle A x = x) - ( λ x → is-in-subtype subtype-descent-data-circle-subtype (pr1 x)) + by inv-associative-Σ equiv-section-descent-data-circle-subtype-fixpoint-in-subtype : dependent-universal-property-circle l → diff --git a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md index 1e014f974d..f3580c570c 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md @@ -123,14 +123,8 @@ module _ ( cofork-cocone-sequential-diagram c)) pr1 equiv-double-arrow-flattening-lemma-sequential-colimit = inv-associative-Σ - ( ℕ) - ( family-sequential-diagram A) - ( P ∘ ind-Σ (map-cocone-sequential-diagram c)) pr1 (pr2 equiv-double-arrow-flattening-lemma-sequential-colimit) = inv-associative-Σ - ( ℕ) - ( family-sequential-diagram A) - ( P ∘ ind-Σ (map-cocone-sequential-diagram c)) pr1 (pr2 (pr2 equiv-double-arrow-flattening-lemma-sequential-colimit)) = refl-htpy pr2 (pr2 (pr2 equiv-double-arrow-flattening-lemma-sequential-colimit)) = diff --git a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md index 10609483e0..4ad46b4c42 100644 --- a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md +++ b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md @@ -219,11 +219,7 @@ module _ ( ( ( left-unit-law-Σ-is-contr ( is-torsorial-Id' (a ∙ a)) ( a ∙ a , refl)) ∘e - ( inv-associative-Σ - ( type-Ω (Ω A)) - ( λ b → b = (a ∙ a)) - ( λ bq → - power-nat-Ω 5 (Ω A) a = power-nat-Ω 3 (Ω A) (pr1 bq)))) ∘e + ( inv-associative-Σ)) ∘e ( equiv-tot ( λ b → ( commutative-product) ∘e diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index bab47be956..5e81600a0b 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -156,12 +156,7 @@ module _ ℤ-Pointed-Type-With-Aut)))) ( is-equiv-id)))) ∘e ( ( equiv-right-swap-Σ) ∘e - ( ( associative-Σ - ( ℤ ≃ ℤ) - ( λ e → Id (map-equiv e zero-ℤ) zero-ℤ) - ( λ e → - ( map-equiv (pr1 e) ∘ succ-ℤ) ~ - ( succ-ℤ ∘ map-equiv (pr1 e)))) ∘e + ( ( associative-Σ) ∘e ( ( equiv-right-swap-Σ) ∘e ( equiv-Σ ( λ e → Id (map-equiv (pr1 e) zero-ℤ) zero-ℤ) diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md index a8b0a7025c..a130c79464 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md @@ -146,19 +146,9 @@ module _ ( left-unit-law-Σ-is-contr ( is-torsorial-Id (point-Pointed-Type Y)) ( point-Pointed-Type Y , refl)) ∘e - ( inv-associative-Σ - ( type-Pointed-Type Y) - ( λ z → point-Pointed-Type Y = z) - ( λ t → - Σ ( type-Pointed-Type X → point-Pointed-Type Y = pr1 t) - ( λ f → f (point-Pointed-Type X) = pr2 t))) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot (λ y1 → equiv-left-swap-Σ)) ∘e - ( associative-Σ - ( type-Pointed-Type Y) - ( λ y1 → type-Pointed-Type X → point-Pointed-Type Y = y1) - ( λ z → - Σ ( point-Pointed-Type Y = pr1 z) - ( λ x → pr2 z (point-Pointed-Type X) = x))) ∘e + ( associative-Σ) ∘e ( inv-right-unit-law-Σ-is-contr ( λ z → is-torsorial-Id (pr2 z (point-Pointed-Type X)))) ∘e ( left-unit-law-Σ-is-contr diff --git a/src/trees/directed-trees.lagda.md b/src/trees/directed-trees.lagda.md index 5c60f5b264..576a4937af 100644 --- a/src/trees/directed-trees.lagda.md +++ b/src/trees/directed-trees.lagda.md @@ -476,11 +476,7 @@ module _ ( y , e)) ≃ Σ ( Σ (vertex-Directed-Graph G) (edge-Directed-Graph G x)) ( λ p → walk-Directed-Graph G (pr1 p) r) - by - inv-associative-Σ - ( vertex-Directed-Graph G) - ( edge-Directed-Graph G x) - ( λ p → walk-Directed-Graph G (pr1 p) r) + by inv-associative-Σ ≃ walk-Directed-Graph G y r by left-unit-law-Σ-is-contr diff --git a/src/trees/extensional-w-types.lagda.md b/src/trees/extensional-w-types.lagda.md index 257d84375e..87ffe47bce 100644 --- a/src/trees/extensional-w-types.lagda.md +++ b/src/trees/extensional-w-types.lagda.md @@ -135,10 +135,7 @@ module _ ( equiv-tot ( λ g → inv-equiv (equiv-fam-equiv-equiv-slice f g)))))) ∘e - ( associative-Σ - ( A) - ( λ x → B x → 𝕎 A B) - ( λ t → Eq-ext-𝕎 (tree-𝕎 a f) (tree-𝕎 (pr1 t) (pr2 t))))) ∘e + ( associative-Σ)) ∘e ( equiv-Σ ( λ (t : Σ A (λ x → B x → 𝕎 A B)) → Eq-ext-𝕎 (tree-𝕎 a f) (tree-𝕎 (pr1 t) (pr2 t))) diff --git a/src/trees/functoriality-w-types.lagda.md b/src/trees/functoriality-w-types.lagda.md index 6a32e1a93e..e5a123d283 100644 --- a/src/trees/functoriality-w-types.lagda.md +++ b/src/trees/functoriality-w-types.lagda.md @@ -71,10 +71,7 @@ abstract (D : C → UU l4) (f : A → C) (e : (x : A) → B x ≃ D (f x)) → (y : 𝕎 C D) → fiber (map-𝕎 D f e) y ≃ fiber-map-𝕎 D f e y equiv-fiber-map-𝕎 {A = A} {B} {C} D f e (tree-𝕎 c γ) = - ( ( ( inv-equiv - ( associative-Σ A - ( λ a → f a = c) - ( λ t → (d : D c) → fiber (map-𝕎 D f e) (γ d)))) ∘e + ( ( ( inv-associative-Σ) ∘e ( equiv-tot ( λ a → ( ( equiv-tot @@ -110,9 +107,7 @@ abstract ( f a) ( ( map-𝕎 D f e) ∘ ( α ∘ map-inv-equiv (e a)))) (tree-𝕎 c γ)))))) ∘e - ( associative-Σ A - ( λ a → B a → 𝕎 A B) - ( λ t → map-𝕎 D f e (structure-𝕎-Alg t) = tree-𝕎 c γ))) ∘e + ( associative-Σ)) ∘e ( equiv-Σ ( λ t → map-𝕎 D f e (structure-𝕎-Alg t) = tree-𝕎 c γ) ( inv-equiv-structure-𝕎-Alg) diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index f815dbd237..a2eeb10c7a 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -172,12 +172,9 @@ compute-binomial-type-Level l {l1} {l2} A B = equiv-trunc-Prop ( equiv-postcomp-equiv ( inv-equiv (equiv-total-fiber (pr1 (pr2 e)))) B))) ∘e - ( inv-associative-Σ - ( UU (l1 ⊔ l)) - ( λ X → X ↪ᵈ A) - ( λ X → mere-equiv B (pr1 X)))) ∘e + ( inv-associative-Σ)) ∘e ( equiv-tot (λ X → commutative-product))) ∘e - ( associative-Σ (UU (l1 ⊔ l)) (λ X → mere-equiv B X) (λ X → (pr1 X) ↪ᵈ A)) + ( associative-Σ) compute-binomial-type : {l1 l2 : Level} (A : UU l1) (B : UU l2) → @@ -313,14 +310,7 @@ abstract ( _) ( λ q → id-equiv) ( λ q → id-equiv)))))))) ∘e - ( associative-Σ - ( A → Decidable-Prop _) - ( λ a → Decidable-Prop _) - ( λ t → - mere-equiv - ( Maybe B) - ( ( Σ A (λ a → type-Decidable-Prop (pr1 t a))) + - ( type-Decidable-Prop (pr2 t)))))) ∘e + ( associative-Σ)) ∘e ( equiv-Σ ( λ p → mere-equiv diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index 43dee54458..476f64dd05 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -84,7 +84,7 @@ equiv-left-factor {l1} {l2} {X} {Y} y = ( ( right-unit-law-product) ∘e ( equiv-tot ( λ x → equiv-is-contr (is-torsorial-Id' y) is-contr-unit))) ∘e - ( associative-Σ X (λ x → Y) (λ t → Id (pr2 t) y)) + ( associative-Σ) count-left-factor : {l1 l2 : Level} {X : UU l1} {Y : UU l2} → count (X × Y) → Y → count X diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index 398a1fe35d..fd404527f3 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -148,9 +148,7 @@ count-fiber-map-section-family {l1} {l2} {A} {B} b e f (pair y z) = ( ( ( left-unit-law-Σ-is-contr ( is-torsorial-Id' y) ( pair y refl)) ∘e - ( inv-associative-Σ A - ( λ x → Id x y) - ( λ t → Id (tr B (pr2 t) (b (pr1 t))) z))) ∘e + ( inv-associative-Σ)) ∘e ( equiv-tot (λ x → equiv-pair-eq-Σ (pair x (b x)) (pair y z)))) ( count-eq (has-decidable-equality-count (f y)) (b y) z) diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index c623cec35a..04f24d2510 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -187,12 +187,7 @@ equiv-Surjection-Finite-Type-Decidable-Equivalence-Relation-Finite-Type {l1} A = ( λ X → (type-Finite-Type A) ↠ (type-Finite-Type X)) ( equiv-tot ( λ X → inv-equiv is-finite-iff-∃-surjection-has-decidable-equality))) ∘e - ( inv-associative-Σ - ( UU l1) - ( λ X → - has-decidable-equality X × - type-trunc-Prop (Σ ℕ (λ n → Fin n ↠ X))) - ( λ X → type-Finite-Type A ↠ pr1 X)) ∘e + ( inv-associative-Σ) ∘e ( equiv-tot ( λ X → ( ( inv-equiv diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index bb19fd3a96..3e240adc0c 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -108,9 +108,7 @@ abstract ( λ t → ( equiv-tot ( λ x → equiv-eq-pair-Σ (map-section-family b x) t)) ∘e - ( ( associative-Σ A - ( λ (x : A) → Id x (pr1 t)) - ( λ s → Id (tr B (pr2 s) (b (pr1 s))) (pr2 t))) ∘e + ( ( associative-Σ) ∘e ( inv-left-unit-law-Σ-is-contr ( is-torsorial-Id' (pr1 t)) ( pair (pr1 t) refl)))))) diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 2d9e458ea5..8a78ffba0b 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -121,9 +121,7 @@ abstract ( ( ( left-unit-law-Σ-is-contr ( is-torsorial-Id' y) ( pair y refl)) ∘e - ( inv-associative-Σ A - ( λ x → Id x y) - ( λ t → Id (tr B (pr2 t) (b (pr1 t))) z))) ∘e + ( inv-associative-Σ)) ∘e ( equiv-tot (λ x → equiv-pair-eq-Σ (pair x (b x)) (pair y z)))) ( is-finite-eq (has-decidable-equality-is-finite (g y))) ``` diff --git a/src/univalent-combinatorics/inhabited-finite-types.lagda.md b/src/univalent-combinatorics/inhabited-finite-types.lagda.md index 8fb4593a19..62ad690ee5 100644 --- a/src/univalent-combinatorics/inhabited-finite-types.lagda.md +++ b/src/univalent-combinatorics/inhabited-finite-types.lagda.md @@ -87,17 +87,17 @@ is-finite-and-inhabited X = compute-Inhabited-Finite-Type' : {l : Level} → Inhabited-Finite-Type l ≃ type-subuniverse is-finite-and-inhabited-Prop -compute-Inhabited-Finite-Type' = associative-Σ _ _ _ +compute-Inhabited-Finite-Type' = associative-Σ map-compute-Inhabited-Finite-Type' : {l : Level} → Inhabited-Finite-Type l → type-subuniverse is-finite-and-inhabited-Prop -map-compute-Inhabited-Finite-Type' = map-associative-Σ _ _ _ +map-compute-Inhabited-Finite-Type' = map-associative-Σ map-inv-compute-Inhabited-Finite-Type' : {l : Level} → type-subuniverse is-finite-and-inhabited-Prop → Inhabited-Finite-Type l -map-inv-compute-Inhabited-Finite-Type' = map-inv-associative-Σ _ _ _ +map-inv-compute-Inhabited-Finite-Type' = map-inv-associative-Σ ``` ### Families of inhabited types diff --git a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md index 6fff4532d6..c610429e47 100644 --- a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md @@ -51,7 +51,7 @@ abstract ( ( double-counting-equiv ( count-Σ count-A (λ x → count-Σ (count-B x) (λ y → count-Fin (f x y)))) ( count-Σ (count-Σ count-A count-B) (λ x → count-Fin (ind-Σ f x))) - ( inv-associative-Σ A B (λ x → Fin (ind-Σ f x)))) ∙ + ( inv-associative-Σ)) ∙ ( number-of-elements-count-Σ ( count-Σ count-A count-B) ( λ x → (count-Fin (ind-Σ f x))))) diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index bdfc816854..77a5a6feee 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -53,7 +53,7 @@ equiv-surjection-finite-type-family-finite-inhabited-type {l} A B = Σ (type-Finite-Type B) (λ b → type-Inhabited-Finite-Type (Y b))) ( equiv-postcomp ( type-Finite-Type B) - ( inv-associative-Σ ( UU l) is-finite ( λ X → is-inhabited (pr1 X)) ∘e + ( inv-associative-Σ) ∘e equiv-Σ ( λ z → is-finite z × is-inhabited z) ( id-equiv) @@ -67,10 +67,7 @@ equiv-surjection-finite-type-family-finite-inhabited-type {l} A B = ( structure-map (λ x → is-inhabited x × is-finite x)) ( id-equiv) ( λ _ → inv-equiv distributive-Π-Σ)) ∘e - ( ( associative-Σ - ( type-Finite-Type A → type-Finite-Type B) - ( structure-map is-inhabited) - ( _)) ∘e + ( ( associative-Σ) ∘e ( ( inv-equiv ( equiv-inclusion-is-full-subtype ( λ f → @@ -96,7 +93,7 @@ equiv-Fiber-trunc-prop-Finite-Type l {l1} A = ( ( equiv-Π ( λ _ → Inhabited-Finite-Type _) ( id-equiv) - ( λ a → inv-associative-Σ _ _ _) ∘e + ( λ a → inv-associative-Σ) ∘e ( ( equiv-Fiber-structure ( l) ( λ X → is-finite X × is-inhabited X) (type-Finite-Type A)))) ∘e @@ -117,5 +114,5 @@ equiv-Fiber-trunc-prop-Finite-Type l {l1} A = ( _) ( id-equiv) ( λ _ → equiv-left-swap-Σ)) ∘e - ( associative-Σ (UU (l ⊔ l1)) (is-finite) _))))) + ( associative-Σ))))) ``` From 1992ad505636deb44f0f273989a9edbfbb25fd60 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:19:58 +0200 Subject: [PATCH 02/13] implicit type arguments for `associative-product` --- .../iterated-cartesian-product-types.lagda.md | 9 ++------- ...type-arithmetic-cartesian-product-types.lagda.md | 2 +- ...oducts-species-of-types-in-subuniverses.lagda.md | 4 ++-- ...oducts-species-of-types-in-subuniverses.lagda.md | 7 +++---- .../decidable-equivalence-relations.lagda.md | 13 +++---------- 5 files changed, 11 insertions(+), 24 deletions(-) diff --git a/src/foundation/iterated-cartesian-product-types.lagda.md b/src/foundation/iterated-cartesian-product-types.lagda.md index e51230c990..8dfdd371b9 100644 --- a/src/foundation/iterated-cartesian-product-types.lagda.md +++ b/src/foundation/iterated-cartesian-product-types.lagda.md @@ -131,13 +131,8 @@ equiv-product-iterated-product-lists : equiv-product-iterated-product-lists nil q = left-unit-law-product-is-contr (is-contr-raise-unit) equiv-product-iterated-product-lists (cons x p) q = - ( ( equiv-product - ( id-equiv) - ( equiv-product-iterated-product-lists p q)) ∘e - ( associative-product - ( x) - ( iterated-product-lists p) - ( iterated-product-lists q))) + ( equiv-product-right (equiv-product-iterated-product-lists p q)) ∘e + ( associative-product) ``` ### Iterated cartesian product is closed under permutations diff --git a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md index 80593c1a75..d4848eb164 100644 --- a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md +++ b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md @@ -69,7 +69,7 @@ module _ ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : UU l2) (C : UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} where map-associative-product : (A × B) × C → A × (B × C) diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index 487ad89689..a6fc56374c 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -165,14 +165,14 @@ module _ P X d)))) ( ( equiv-Σ ( _) - ( associative-product _ _ _ ∘e commutative-product) + ( associative-product ∘e commutative-product) ( λ x → equiv-postcomp-equiv ( associative-coproduct ∘e commutative-coproduct _ _) ( inclusion-subuniverse P X))) ∘e ( equiv-ternary-left-iterated-coproduct-Decomposition-subuniverse P X C2)) - ( λ d → associative-product _ _ _)) ∘e + ( λ d → associative-product)) ∘e ( inv-associative-Σ) ∘e ( equiv-tot (λ d → right-distributive-product-Σ)) diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index 89560cf1ab..b77419e7b6 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -183,17 +183,16 @@ module _ d)))) ( equiv-Σ ( _) - ( associative-product _ _ _ ∘e commutative-product) + ( associative-product ∘e commutative-product) ( λ x → equiv-postcomp-equiv - ( ( associative-product _ _ _ ∘e - ( commutative-product))) + ( associative-product ∘e commutative-product) ( inclusion-subuniverse P X)) ∘e equiv-ternary-left-iterated-product-Decomposition-Subuniverse P X C2) - ( λ d → associative-product _ _ _)) ∘e + ( λ d → associative-product)) ∘e ( inv-associative-Σ) ∘e ( equiv-tot (λ d → right-distributive-product-Σ)) diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index 04f24d2510..a792a83eff 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -190,16 +190,9 @@ equiv-Surjection-Finite-Type-Decidable-Equivalence-Relation-Finite-Type {l1} A = ( inv-associative-Σ) ∘e ( equiv-tot ( λ X → - ( ( inv-equiv - ( associative-product - ( has-decidable-equality X) - ( type-trunc-Prop (Σ ℕ (λ n → Fin n ↠ X))) - ( type-Finite-Type A ↠ X))) ∘e - ( equiv-product id-equiv commutative-product) ∘e - ( associative-product - ( has-decidable-equality (map-equiv id-equiv X)) - ( type-Finite-Type A ↠ X) - ( type-trunc-Prop (Σ ℕ (λ n → Fin n ↠ X)))) ∘e + ( ( inv-associative-product) ∘e + ( equiv-product-right commutative-product) ∘e + ( associative-product) ∘e ( equiv-product-left commutative-product) ∘e ( equiv-add-redundant-prop ( is-prop-type-trunc-Prop) From a0980144db93fdaa214095df1bb2d5bc199f5f9b Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:23:10 +0200 Subject: [PATCH 03/13] implicit type arguments for `commutative-coproduct` --- .../coproduct-decompositions-subuniverse.lagda.md | 8 +++----- src/foundation/disjunction.lagda.md | 2 +- src/foundation/type-arithmetic-coproduct-types.lagda.md | 2 +- ...chy-products-species-of-types-in-subuniverses.lagda.md | 2 +- .../2-element-decidable-subtypes.lagda.md | 5 +---- .../finitely-enumerable-types.lagda.md | 2 +- 6 files changed, 8 insertions(+), 13 deletions(-) diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index 290062c879..a86fec7fd1 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -300,10 +300,8 @@ module _ ( commutative-product) ( λ x → equiv-postcomp-equiv - ( commutative-coproduct - ( inclusion-subuniverse P (pr1 x)) - ( inclusion-subuniverse P (pr2 x))) - (inclusion-subuniverse P X))) ∘e + ( commutative-coproduct) + ( inclusion-subuniverse P X))) ∘e ( ( inv-associative-Σ))) ``` @@ -378,7 +376,7 @@ module _ ( equiv-tot ( λ x → ( ( equiv-postcomp-equiv - ( commutative-coproduct _ _) + ( commutative-coproduct) ( inclusion-subuniverse P X)) ∘e ( ( left-unit-law-Σ-is-contr ( is-torsorial-equiv-subuniverse' P diff --git a/src/foundation/disjunction.lagda.md b/src/foundation/disjunction.lagda.md index a36b44f3f7..042a708468 100644 --- a/src/foundation/disjunction.lagda.md +++ b/src/foundation/disjunction.lagda.md @@ -346,7 +346,7 @@ module _ where swap-disjunction : disjunction-type A B → disjunction-type B A - swap-disjunction = map-trunc-Prop (map-commutative-coproduct A B) + swap-disjunction = map-trunc-Prop map-commutative-coproduct ``` ## See also diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 4bfa836a20..03ee263c6c 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -34,7 +34,7 @@ themselves, cartesian products, and dependent pair types. ```agda module _ - {l1 l2 : Level} (A : UU l1) (B : UU l2) + {l1 l2 : Level} {A : UU l1} {B : UU l2} where map-commutative-coproduct : A + B → B + A diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index a6fc56374c..0f01710cdb 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -168,7 +168,7 @@ module _ ( associative-product ∘e commutative-product) ( λ x → equiv-postcomp-equiv - ( associative-coproduct ∘e commutative-coproduct _ _) + ( associative-coproduct ∘e commutative-coproduct) ( inclusion-subuniverse P X))) ∘e ( equiv-ternary-left-iterated-coproduct-Decomposition-subuniverse P X C2)) diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index f223fc9b23..fe3efa9178 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -221,10 +221,7 @@ module _ ( eq-htpy (λ z → eq-pair-Σ - ( eq-equiv - ( pair - ( map-commutative-coproduct (Id x z) (Id y z)) - ( is-equiv-map-commutative-coproduct (Id x z) (Id y z)))) + ( eq-equiv commutative-coproduct) ( eq-pair-Σ ( eq-is-prop ( is-prop-is-prop diff --git a/src/univalent-combinatorics/finitely-enumerable-types.lagda.md b/src/univalent-combinatorics/finitely-enumerable-types.lagda.md index 11cc061fef..0641d57932 100644 --- a/src/univalent-combinatorics/finitely-enumerable-types.lagda.md +++ b/src/univalent-combinatorics/finitely-enumerable-types.lagda.md @@ -238,7 +238,7 @@ abstract finite-enumeration (X + Y) → finite-enumeration Y finite-enumeration-right-summand eX+Y = finite-enumeration-left-summand - ( finite-enumeration-equiv eX+Y (commutative-coproduct _ _)) + ( finite-enumeration-equiv eX+Y (commutative-coproduct)) finite-enumeration-coproduct : {l1 l2 : Level} {X : UU l1} {Y : UU l2} → From f6b93a33b01c3c899d72fa79833974a97a0f153c Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:30:37 +0200 Subject: [PATCH 04/13] fix `inv-associative-product` --- .../type-arithmetic-cartesian-product-types.lagda.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md index d4848eb164..6125780a0c 100644 --- a/src/foundation/type-arithmetic-cartesian-product-types.lagda.md +++ b/src/foundation/type-arithmetic-cartesian-product-types.lagda.md @@ -94,6 +94,9 @@ module _ associative-product : ((A × B) × C) ≃ (A × (B × C)) associative-product = associative-Σ + + inv-associative-product : (A × (B × C)) ≃ ((A × B) × C) + inv-associative-product = inv-associative-Σ ``` ### The unit laws of cartesian product types with respect to contractible types From b89b76dfebe0ae0a19073cf198fc354e389a07a4 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:40:13 +0200 Subject: [PATCH 05/13] =?UTF-8?q?implicit=20type=20arguments=20to=20`right?= =?UTF-8?q?-distributive-=CE=A3-coproduct`?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...ring-principle-standard-finite-types.lagda.md | 2 +- ...w-coproduct-and-sigma-decompositions.lagda.md | 2 +- src/foundation/coproduct-decompositions.lagda.md | 16 +--------------- .../decidable-dependent-pair-types.lagda.md | 2 +- src/foundation/exclusive-disjunction.lagda.md | 2 -- src/foundation/exclusive-sum.lagda.md | 4 ---- .../type-arithmetic-coproduct-types.lagda.md | 14 +++++++------- ...lies-of-elements-commutative-monoids.lagda.md | 10 ++-------- .../flattening-lemma-coequalizers.lagda.md | 2 -- .../2-element-types.lagda.md | 2 +- .../binomial-types.lagda.md | 8 ++------ .../counting-decidable-subtypes.lagda.md | 10 ++-------- .../counting-dependent-pair-types.lagda.md | 2 +- .../untruncated-pi-finite-types.lagda.md | 5 +---- 14 files changed, 20 insertions(+), 61 deletions(-) diff --git a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md index c8d6c7ef26..ae462be745 100644 --- a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md @@ -242,6 +242,6 @@ abstract ( Σ (Fin k) (B ∘ inl)) ( B (inr star)) f) ∘e ( equiv-coproduct id-equiv (left-unit-law-Σ (B ∘ inr)))) ∘e - ( right-distributive-Σ-coproduct (Fin k) unit B)) + ( right-distributive-Σ-coproduct B)) ( y))) ``` diff --git a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md index c29be5ba4a..5790b0d216 100644 --- a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md @@ -138,7 +138,7 @@ module _ ( ( equiv-tot ( λ Y → equiv-postcomp-equiv - ( right-distributive-Σ-coproduct A B Y) + ( right-distributive-Σ-coproduct Y) ( X))) ∘e ( left-unit-law-Σ-is-contr ( is-torsorial-equiv' (A + B)) diff --git a/src/foundation/coproduct-decompositions.lagda.md b/src/foundation/coproduct-decompositions.lagda.md index 4f8dfd14be..081d474d3f 100644 --- a/src/foundation/coproduct-decompositions.lagda.md +++ b/src/foundation/coproduct-decompositions.lagda.md @@ -246,7 +246,7 @@ module _ ( ( equiv-coproduct ( left-unit-law-Σ-is-contr ( is-contr-Fin-1) ( inr star)) ( left-unit-law-Σ-is-contr is-contr-unit star)) ∘e - ( ( right-distributive-Σ-coproduct ( Fin 1) unit (λ x → fiber f x) ∘e + ( ( right-distributive-Σ-coproduct (λ x → fiber f x) ∘e ( inv-equiv-total-fiber f)))) compute-left-matching-correspondence-binary-coproduct-Decomposition-map-into-Fin-Two-ℕ : @@ -272,8 +272,6 @@ module _ ( inr star)) ( map-left-unit-law-Σ-is-contr is-contr-unit star)) ( map-right-distributive-Σ-coproduct - ( Fin 1) - ( unit) ( λ x → fiber f x) ( pr1 a , x , pr2 a)))) ( λ z → pr1 (pr1 z) = x)) @@ -335,8 +333,6 @@ module _ ( inr star)) ( map-left-unit-law-Σ-is-contr is-contr-unit star)) ( map-right-distributive-Σ-coproduct - ( Fin 1) - ( unit) ( λ x → fiber f x) ( pr1 a , x , pr2 a)))) ( λ z → pr1 (pr1 z) = x)) @@ -519,8 +515,6 @@ module _ ( map-left-unit-law-Σ-is-contr is-contr-Fin-1 ( inr star)) ( map-left-unit-law-Σ-is-contr is-contr-unit star) ( map-right-distributive-Σ-coproduct - ( Fin 1) - ( unit) ( λ y → y = f x) ( f x , refl)))) @@ -543,8 +537,6 @@ module _ equiv-tot ( λ _ → extensionality-Fin 2 (inr star) (inl (inr star))))) ∘e ( ( right-distributive-Σ-coproduct - ( left-summand-binary-coproduct-Decomposition d) - ( right-summand-binary-coproduct-Decomposition d) ( λ y → map-inv-equiv-binary-coproduct-Decomposition-map-into-Fin-Two-ℕ-helper d y = inl (inr star))) ∘e @@ -573,8 +565,6 @@ module _ equiv-tot ( λ _ → extensionality-Fin 2 (inr star) (inr star)))) ∘e ( ( right-distributive-Σ-coproduct - ( left-summand-binary-coproduct-Decomposition d) - ( right-summand-binary-coproduct-Decomposition d) ( λ y → map-inv-equiv-binary-coproduct-Decomposition-map-into-Fin-Two-ℕ-helper d y = inr star)) ∘e @@ -612,8 +602,6 @@ module _ ( λ _ → extensionality-Fin 2 (inr star) (inl (inr star))))) ∘e ( ( right-distributive-Σ-coproduct - ( left-summand-binary-coproduct-Decomposition d) - ( right-summand-binary-coproduct-Decomposition d) ( λ y → map-inv-equiv-binary-coproduct-Decomposition-map-into-Fin-Two-ℕ-helper d y = @@ -667,8 +655,6 @@ module _ equiv-tot ( λ _ → extensionality-Fin 2 (inr star) (inr star)))) ∘e ( ( right-distributive-Σ-coproduct - ( left-summand-binary-coproduct-Decomposition d) - ( right-summand-binary-coproduct-Decomposition d) ( λ y → map-inv-equiv-binary-coproduct-Decomposition-map-into-Fin-Two-ℕ-helper d y = inr star))))) diff --git a/src/foundation/decidable-dependent-pair-types.lagda.md b/src/foundation/decidable-dependent-pair-types.lagda.md index 401e13a607..01a42bb150 100644 --- a/src/foundation/decidable-dependent-pair-types.lagda.md +++ b/src/foundation/decidable-dependent-pair-types.lagda.md @@ -78,7 +78,7 @@ is-decidable-Σ-coproduct : is-decidable (Σ (A + B) C) is-decidable-Σ-coproduct {A = A} {B} C dA dB = is-decidable-equiv - ( right-distributive-Σ-coproduct A B C) + ( right-distributive-Σ-coproduct C) ( is-decidable-coproduct dA dB) ``` diff --git a/src/foundation/exclusive-disjunction.lagda.md b/src/foundation/exclusive-disjunction.lagda.md index 92407933be..f64452e516 100644 --- a/src/foundation/exclusive-disjunction.lagda.md +++ b/src/foundation/exclusive-disjunction.lagda.md @@ -162,8 +162,6 @@ module _ ( is-prop-type-Prop Q q q'))))) ∘e ( equiv-dependent-universal-property-coproduct (inr q =_))))) ∘e ( right-distributive-Σ-coproduct - ( type-Prop P) - ( type-Prop Q) ( λ x → (y : type-Prop P + type-Prop Q) → x = y)) ``` diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index 7282c9e05d..5683503a4f 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -250,8 +250,6 @@ module _ ( pr1 (standard-unordered-pair P Q)) ( inl (inr y))))))))))) ∘e ( ( right-distributive-Σ-coproduct - ( Fin 0) - ( unit) ( λ x → ( type-Prop (pr2 (standard-unordered-pair P Q) (inl x))) × ( ¬ ( type-Prop @@ -278,8 +276,6 @@ module _ ( pr1 (standard-unordered-pair P Q)) ( inr y)))))))))) ∘e ( right-distributive-Σ-coproduct - ( Fin 1) - ( unit) ( λ x → ( type-Prop (pr2 (standard-unordered-pair P Q) x)) × ( ¬ ( type-Prop diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 03ee263c6c..aaf4dff94b 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -124,7 +124,7 @@ module _ ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : UU l2) (C : A + B → UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (C : A + B → UU l3) where map-right-distributive-Σ-coproduct : @@ -225,34 +225,34 @@ module _ map-right-distributive-product-coproduct : (A + B) × C → (A × C) + (B × C) map-right-distributive-product-coproduct = - map-right-distributive-Σ-coproduct A B (λ _ → C) + map-right-distributive-Σ-coproduct (λ _ → C) map-inv-right-distributive-product-coproduct : (A × C) + (B × C) → (A + B) × C map-inv-right-distributive-product-coproduct = - map-inv-right-distributive-Σ-coproduct A B (λ _ → C) + map-inv-right-distributive-Σ-coproduct (λ _ → C) is-section-map-inv-right-distributive-product-coproduct : map-right-distributive-product-coproduct ∘ map-inv-right-distributive-product-coproduct ~ id is-section-map-inv-right-distributive-product-coproduct = - is-section-map-inv-right-distributive-Σ-coproduct A B (λ _ → C) + is-section-map-inv-right-distributive-Σ-coproduct (λ _ → C) is-retraction-map-inv-right-distributive-product-coproduct : map-inv-right-distributive-product-coproduct ∘ map-right-distributive-product-coproduct ~ id is-retraction-map-inv-right-distributive-product-coproduct = - is-retraction-map-inv-right-distributive-Σ-coproduct A B (λ _ → C) + is-retraction-map-inv-right-distributive-Σ-coproduct (λ _ → C) abstract is-equiv-map-right-distributive-product-coproduct : is-equiv map-right-distributive-product-coproduct is-equiv-map-right-distributive-product-coproduct = - is-equiv-map-right-distributive-Σ-coproduct A B (λ _ → C) + is-equiv-map-right-distributive-Σ-coproduct (λ _ → C) right-distributive-product-coproduct : ((A + B) × C) ≃ ((A × C) + (B × C)) right-distributive-product-coproduct = - right-distributive-Σ-coproduct A B (λ _ → C) + right-distributive-Σ-coproduct (λ _ → C) ``` ### Left distributivity of products over coproducts diff --git a/src/group-theory/sums-of-finite-families-of-elements-commutative-monoids.lagda.md b/src/group-theory/sums-of-finite-families-of-elements-commutative-monoids.lagda.md index 1554075883..c27c776f25 100644 --- a/src/group-theory/sums-of-finite-families-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/sums-of-finite-families-of-elements-commutative-monoids.lagda.md @@ -580,10 +580,7 @@ module _ map-coproduct ( id) ( map-left-unit-law-Σ (type-Finite-Type ∘ B ∘ inr)) ∘ - map-right-distributive-Σ-coproduct - ( Fin n) - ( unit) - ( type-Finite-Type ∘ B)) + map-right-distributive-Σ-coproduct (type-Finite-Type ∘ B)) by sum-equiv-finite-Commutative-Monoid ( M) @@ -595,10 +592,7 @@ module _ ( equiv-coproduct ( id-equiv) ( left-unit-law-Σ (type-Finite-Type ∘ B ∘ inr)) ∘e - right-distributive-Σ-coproduct - ( Fin n) - ( unit) - ( type-Finite-Type ∘ B))) + right-distributive-Σ-coproduct (type-Finite-Type ∘ B))) _ = sum-finite-Commutative-Monoid diff --git a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md index abddcc385a..a42dcdfe4c 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md @@ -167,8 +167,6 @@ module _ ( horizontal-map-span-cocone-cofork a) ( cocone-codiagonal-cofork a e)) ( right-distributive-Σ-coproduct - ( domain-double-arrow a) - ( domain-double-arrow a) ( ( P) ∘ ( horizontal-map-cocone-cofork a e) ∘ ( vertical-map-span-cocone-cofork a))) diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index b44650d1ca..94d03c1ac9 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -784,7 +784,7 @@ is-coproduct-Σ-Fin-2 P = ( equiv-coproduct ( left-unit-law-Σ-is-contr is-contr-Fin-1 (zero-Fin 0)) ( left-unit-law-Σ (P ∘ inr))) ∘e - ( right-distributive-Σ-coproduct (Fin 1) unit P) + ( right-distributive-Σ-coproduct P) ``` ### For any equivalence `e : Fin 2 ≃ X`, any element of `X` is either `e 0` or it is `e 1` diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index a2eeb10c7a..f078d91c5e 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -280,15 +280,11 @@ abstract ( is-torsorial-false-Prop) ( pair (raise-empty-Prop _) map-inv-raise)))) ∘e ( right-distributive-Σ-coproduct - ( Σ (Prop _) type-Prop) - ( Σ (Prop _) (¬_ ∘ type-Prop)) ( ind-coproduct _ ( λ Q → mere-equiv (Maybe B) ((Σ A _) + (type-Prop (pr1 Q)))) ( λ Q → - mere-equiv - ( Maybe B) - ( (Σ A _) + (type-Prop (pr1 Q))))))) ∘e + mere-equiv (Maybe B) ((Σ A _) + (type-Prop (pr1 Q))))))) ∘e ( equiv-Σ ( ind-coproduct _ ( λ Q → @@ -324,7 +320,7 @@ abstract ( ( equiv-coproduct ( id-equiv) ( left-unit-law-Σ (λ y → type-Decidable-Prop (u (inr y))))) ∘e - ( right-distributive-Σ-coproduct A unit + ( right-distributive-Σ-coproduct ( λ x → type-Decidable-Prop (u x)))) ( Maybe B)))) diff --git a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md index 6b06dd1332..b8b4c7ba7c 100644 --- a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md @@ -55,10 +55,7 @@ abstract with is-decidable-decidable-subtype P (inr star) ... | inl p = count-equiv' - ( right-distributive-Σ-coproduct - ( Fin k) - ( unit) - ( is-in-decidable-subtype P)) + ( right-distributive-Σ-coproduct (is-in-decidable-subtype P)) ( pair ( succ-ℕ ( number-of-elements-count (count-decidable-subtype-Fin k (P ∘ inl)))) @@ -70,10 +67,7 @@ abstract ( is-proof-irrelevant-is-in-decidable-subtype P (inr star) p))))) ... | inr f = count-equiv' - ( right-distributive-Σ-coproduct - ( Fin k) - ( unit) - ( is-in-decidable-subtype P)) + ( right-distributive-Σ-coproduct (is-in-decidable-subtype P)) ( count-equiv' ( right-unit-law-coproduct-is-empty ( Σ (Fin k) (is-in-decidable-subtype P ∘ inl)) diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index fd404527f3..91f8dc7831 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -67,7 +67,7 @@ count-Σ-Fin 0 f = count-is-empty pr1 count-Σ-Fin (succ-ℕ k) {B} f = count-equiv' ( ( equiv-coproduct id-equiv (left-unit-law-Σ (B ∘ inr))) ∘e - ( right-distributive-Σ-coproduct (Fin k) unit B)) + ( right-distributive-Σ-coproduct B)) ( count-coproduct (count-Σ-Fin k (f ∘ inl)) (f (inr star))) count-Σ' : diff --git a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md index 716344eb21..1977ebdaf6 100644 --- a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md @@ -620,10 +620,7 @@ abstract ( refl-htpy)) ( λ { (inl x) → id-equiv ; (inr x) → id-equiv})) ∘e ( inv-equiv - ( right-distributive-Σ-coproduct - ( im (f ∘ inl)) - ( im (f ∘ inr)) - ( rec-coproduct (B ∘ pr1) (B ∘ pr1)))) + ( right-distributive-Σ-coproduct (rec-coproduct (B ∘ pr1) (B ∘ pr1)))) i : Fin k → type-trunc-Set (im (f ∘ inl)) i = unit-trunc-Set ∘ map-unit-im (f ∘ inl) From fa9313e0141812e08bd1455d19b94a3b6f191438 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:41:12 +0200 Subject: [PATCH 06/13] implicit type arguments to `right-distributive-product-coproduct` --- .../type-arithmetic-natural-numbers.lagda.md | 8 ++++---- src/foundation/type-arithmetic-coproduct-types.lagda.md | 2 +- .../cartesian-product-types.lagda.md | 2 +- 3 files changed, 6 insertions(+), 6 deletions(-) diff --git a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md index 9d3fa6833f..cc48c40cab 100644 --- a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md +++ b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md @@ -206,12 +206,12 @@ equiv-coproduct-Fin-ℕ (succ-ℕ n) = equiv-product-Fin-ℕ : (n : ℕ) → ((Fin (succ-ℕ n)) × ℕ) ≃ ℕ equiv-product-Fin-ℕ zero-ℕ = ( left-unit-law-coproduct ℕ) ∘e - ( ( equiv-coproduct (left-absorption-product ℕ) left-unit-law-product) ∘e - ( right-distributive-product-coproduct empty unit ℕ)) + ( ( equiv-coproduct (left-absorption-product ℕ) left-unit-law-product) ∘e + ( right-distributive-product-coproduct)) equiv-product-Fin-ℕ (succ-ℕ n) = ( ℕ+ℕ≃ℕ) ∘e - ( ( equiv-coproduct (equiv-product-Fin-ℕ n) left-unit-law-product) ∘e - ( right-distributive-product-coproduct (Fin (succ-ℕ n)) unit ℕ)) + ( ( equiv-coproduct (equiv-product-Fin-ℕ n) left-unit-law-product) ∘e + ( right-distributive-product-coproduct)) ``` ### The integers `ℤ` is equivalent to `ℕ` diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index aaf4dff94b..6dfa69a8f1 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -220,7 +220,7 @@ module _ ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : UU l2) (C : UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} where map-right-distributive-product-coproduct : (A + B) × C → (A × C) + (B × C) diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index 476f64dd05..4b60af63a3 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -56,7 +56,7 @@ product-Fin zero-ℕ l = left-absorption-product (Fin l) product-Fin (succ-ℕ k) l = ( ( compute-coproduct-Fin (k *ℕ l) l) ∘e ( equiv-coproduct (product-Fin k l) left-unit-law-product)) ∘e - ( right-distributive-product-coproduct (Fin k) unit (Fin l)) + ( right-distributive-product-coproduct) Fin-mul-ℕ : (k l : ℕ) → (Fin (k *ℕ l)) ≃ ((Fin k) × (Fin l)) Fin-mul-ℕ k l = inv-equiv (product-Fin k l) From a2f848ec9604b1ae168f4e2c5a573ea8fcf0a87e Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:41:35 +0200 Subject: [PATCH 07/13] implicit type arguments to `left-distributive-product-coproduct` --- src/foundation/type-arithmetic-coproduct-types.lagda.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 6dfa69a8f1..252c3dbe2e 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -259,7 +259,7 @@ module _ ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : UU l2) (C : UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} where map-left-distributive-product-coproduct : A × (B + C) → (A × B) + (A × C) From af460f483c80100f39cfd75d99ae2cd4a0c5469a Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:44:29 +0200 Subject: [PATCH 08/13] =?UTF-8?q?implicit=20type=20arguments=20to=20`left-?= =?UTF-8?q?distributive-=CE=A3-coproduct`?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../falling-factorials.lagda.md | 6 +- .../decidable-propositions.lagda.md | 3 +- .../type-arithmetic-coproduct-types.lagda.md | 14 +- .../walks-undirected-graphs.lagda.md | 10 +- .../complements-decidable-subtypes.lagda.md | 5 +- .../binomial-types.lagda.md | 5 +- .../coproduct-types.lagda.md | 2 +- .../counting-dependent-pair-types.lagda.md | 3 +- .../dependent-pair-types.lagda.md | 5 +- website/images/agda_dependency_graph | 21264 ++++++++++++++++ 10 files changed, 21280 insertions(+), 37 deletions(-) create mode 100644 website/images/agda_dependency_graph diff --git a/src/elementary-number-theory/falling-factorials.lagda.md b/src/elementary-number-theory/falling-factorials.lagda.md index a799101a48..d20c06b1e5 100644 --- a/src/elementary-number-theory/falling-factorials.lagda.md +++ b/src/elementary-number-theory/falling-factorials.lagda.md @@ -70,11 +70,7 @@ Fin-falling-factorial-ℕ (succ-ℕ n) (succ-ℕ m) = ( is-decidable-Σ-Fin ( λ x → has-decidable-equality-Fin (map-emb f x) (inr star))))) ∘e - ( ( inv-equiv - ( left-distributive-Σ-coproduct - ( Fin (succ-ℕ m) ↪ Fin (succ-ℕ n)) - ( λ f → fiber (map-emb f) (inr star)) - ( λ f → ¬ (fiber (map-emb f) (inr star))))) ∘e + ( ( inv-equiv left-distributive-Σ-coproduct) ∘e {!!})) ∘e ( equiv-coproduct ( Fin-falling-factorial-ℕ n m) diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index 6bd0b0b964..24c1b8f0c4 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -76,8 +76,7 @@ split-Decidable-Prop : Decidable-Prop l ≃ ((Σ (Prop l) type-Prop) + (Σ (Prop l) (λ Q → ¬ (type-Prop Q)))) split-Decidable-Prop {l} = - ( left-distributive-Σ-coproduct (Prop l) (λ Q → pr1 Q) (λ Q → ¬ (pr1 Q))) ∘e - ( inv-associative-Σ) + left-distributive-Σ-coproduct ∘e inv-associative-Σ ``` ### The type of decidable propositions in universe level `l` is equivalent to the type of booleans diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 252c3dbe2e..c0ebf917fc 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -173,7 +173,7 @@ module _ ```agda module _ - {l1 l2 l3 : Level} (A : UU l1) (B : A → UU l2) (C : A → UU l3) + {l1 l2 l3 : Level} {A : UU l1} {B : A → UU l2} {C : A → UU l3} where map-left-distributive-Σ-coproduct : @@ -264,33 +264,33 @@ module _ map-left-distributive-product-coproduct : A × (B + C) → (A × B) + (A × C) map-left-distributive-product-coproduct = - map-left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + map-left-distributive-Σ-coproduct map-inv-left-distributive-product-coproduct : (A × B) + (A × C) → A × (B + C) map-inv-left-distributive-product-coproduct = - map-inv-left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + map-inv-left-distributive-Σ-coproduct is-section-map-inv-left-distributive-product-coproduct : map-left-distributive-product-coproduct ∘ map-inv-left-distributive-product-coproduct ~ id is-section-map-inv-left-distributive-product-coproduct = - is-section-map-inv-left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + is-section-map-inv-left-distributive-Σ-coproduct is-retraction-map-inv-left-distributive-product-coproduct : map-inv-left-distributive-product-coproduct ∘ map-left-distributive-product-coproduct ~ id is-retraction-map-inv-left-distributive-product-coproduct = - is-retraction-map-inv-left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + is-retraction-map-inv-left-distributive-Σ-coproduct is-equiv-map-left-distributive-product-coproduct : is-equiv map-left-distributive-product-coproduct is-equiv-map-left-distributive-product-coproduct = - is-equiv-map-left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + is-equiv-map-left-distributive-Σ-coproduct left-distributive-product-coproduct : (A × (B + C)) ≃ ((A × B) + (A × C)) left-distributive-product-coproduct = - left-distributive-Σ-coproduct A (λ _ → B) (λ _ → C) + left-distributive-Σ-coproduct ``` ### If a coproduct is contractible then one summand is contractible and the other is empty diff --git a/src/graph-theory/walks-undirected-graphs.lagda.md b/src/graph-theory/walks-undirected-graphs.lagda.md index b73510b8b4..767ae78258 100644 --- a/src/graph-theory/walks-undirected-graphs.lagda.md +++ b/src/graph-theory/walks-undirected-graphs.lagda.md @@ -194,10 +194,7 @@ module _ ( equiv-is-contr ( is-torsorial-Id (other-element-unordered-pair p y)) ( is-contr-unit))) ∘e - ( left-distributive-Σ-coproduct - ( vertex-Undirected-Graph G) - ( is-vertex-on-walk-Undirected-Graph G w) - ( λ z → other-element-unordered-pair p y = z)) + ( left-distributive-Σ-coproduct) ``` ### The type of edges on a constant walk is empty @@ -233,10 +230,7 @@ module _ ( equiv-is-contr ( is-torsorial-Id (pair p e)) ( is-contr-unit))) ∘e - ( left-distributive-Σ-coproduct - ( total-edge-Undirected-Graph G) - ( is-edge-on-walk-Undirected-Graph' G w) - ( λ z → pair p e = z)) + ( left-distributive-Σ-coproduct) ``` ### Right unit law for concatenation of walks diff --git a/src/logic/complements-decidable-subtypes.lagda.md b/src/logic/complements-decidable-subtypes.lagda.md index 44304ffbcd..3af0d7621b 100644 --- a/src/logic/complements-decidable-subtypes.lagda.md +++ b/src/logic/complements-decidable-subtypes.lagda.md @@ -130,8 +130,5 @@ module _ ( is-prop-is-decidable (is-prop-is-in-decidable-subtype P x)) ( is-decidable-decidable-subtype P x)) ≃ type-decidable-subtype P + type-complement-decidable-subtype P - by - left-distributive-Σ-coproduct A - ( is-in-decidable-subtype P) - ( is-in-complement-decidable-subtype P) + by left-distributive-Σ-coproduct ``` diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index f078d91c5e..8b2f68067a 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -247,10 +247,7 @@ abstract binomial-type' (Maybe A) (Maybe B) ≃ (binomial-type' A B + binomial-type' A (Maybe B)) recursion-binomial-type' A B = - ( ( ( left-distributive-Σ-coproduct - ( A → Decidable-Prop _) - ( λ P → mere-equiv B (Σ A _)) - ( λ P → mere-equiv (Maybe B) (Σ A _))) ∘e + ( ( ( left-distributive-Σ-coproduct) ∘e ( equiv-tot ( λ P → ( ( equiv-coproduct diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index ee2c6015ff..ba316d6e83 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -199,7 +199,7 @@ count-Σ-coproduct : count (Σ A P) → count (Σ A Q) → count (Σ A (λ x → (P x) + (Q x))) pr1 (count-Σ-coproduct count-P count-Q) = pr1 (count-coproduct count-P count-Q) pr2 (count-Σ-coproduct count-P count-Q) = - ( inv-equiv (left-distributive-Σ-coproduct _ _ _)) ∘e + ( inv-equiv left-distributive-Σ-coproduct) ∘e ( pr2 (count-coproduct count-P count-Q)) ``` diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index 91f8dc7831..55b38cc930 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -194,8 +194,7 @@ count-base-count-Σ' {l1} {l2} {A} {B} e f g = count-base-count-Σ ( section-count-base-count-Σ' e f g) ( count-equiv' - ( left-distributive-Σ-coproduct A B - ( λ x → is-zero-ℕ (number-of-elements-count (f x)))) + ( left-distributive-Σ-coproduct) ( count-coproduct e g)) ( λ x → count-coproduct diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index 3e240adc0c..bf244e6fd4 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -160,10 +160,7 @@ abstract is-proof-irrelevant-is-prop ( is-property-is-inhabited-or-empty (B x)) ( is-inhabited-or-empty-is-finite (g x)))) ∘e - ( inv-equiv - ( left-distributive-Σ-coproduct A - ( λ x → type-trunc-Prop (B x)) - ( λ x → is-empty (B x))))) + ( inv-equiv left-distributive-Σ-coproduct)) ( is-finite-coproduct ( is-finite-base-is-finite-Σ-merely-inhabited ( is-set-type-subtype (λ x → trunc-Prop _) K) diff --git a/website/images/agda_dependency_graph b/website/images/agda_dependency_graph new file mode 100644 index 0000000000..b9f2415197 --- /dev/null +++ b/website/images/agda_dependency_graph @@ -0,0 +1,21264 @@ +digraph { + K=0.3 bgcolor="#FFFFFF00" 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"category-theory.yoneda-lemma-categories" -> "category-theory.copresheaf-categories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-categories" -> "foundation.category-of-sets" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" [label="" color="#FFFFFF00" fillcolor="#fbca04" height=0.0690558701659274 shape=circle style=filled width=0.0690558701659274] + "category-theory.yoneda-lemma-precategories" -> "category-theory.precategories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" -> "category-theory.copresheaf-categories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" -> "category-theory.representable-functors-precategories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" -> "category-theory.natural-transformations-functors-from-small-to-large-precategories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" -> "category-theory.functors-from-small-to-large-precategories" [arrowhead=none color="#fbca0410"] + "category-theory.yoneda-lemma-precategories" -> "foundation.category-of-sets" [arrowhead=none color="#fbca0410"] + "commutative-algebra.binomial-theorem-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07050222336024897 shape=circle style=filled width=0.07050222336024897] + "commutative-algebra.binomial-theorem-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "linear-algebra.finite-sequences-in-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "ring-theory.binomial-theorem-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "elementary-number-theory.binomial-coefficients" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-rings" -> "commutative-algebra.binomial-theorem-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07121438510526466 shape=circle style=filled width=0.07121438510526466] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "linear-algebra.finite-sequences-in-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "ring-theory.binomial-theorem-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.powers-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.binomial-coefficients" [arrowhead=none color="#3577BB10"] + "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.boolean-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] + "commutative-algebra.boolean-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.boolean-rings" -> "ring-theory.idempotent-elements-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.category-of-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] + "commutative-algebra.category-of-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.category-of-commutative-rings" -> "category-theory.large-categories" [arrowhead=none color="#3577BB10"] + "commutative-algebra.category-of-commutative-rings" -> "category-theory.categories" [arrowhead=none color="#3577BB10"] + "commutative-algebra.category-of-commutative-rings" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.1296303861210299 shape=circle style=filled width=0.1296303861210299] + "commutative-algebra.commutative-rings" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.involutions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.embeddings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.binary-equivalences" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.binary-embeddings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.negation" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "lists.lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09124869666223606 shape=circle style=filled width=0.09124869666223606] + "commutative-algebra.commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-semirings" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-semirings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07846294652976578 shape=circle style=filled width=0.07846294652976578] + "commutative-algebra.convolution-sequences-commutative-rings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> "lists.sequences" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-rings" -> 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color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "lists.sequences" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.function-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "elementary-number-theory.binary-sum-decompositions-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.convolution-sequences-commutative-semirings" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] + "commutative-algebra.dependent-products-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0645225721843014 shape=circle style=filled width=0.0645225721843014] + "commutative-algebra.dependent-products-commutative-rings" -> 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"commutative-algebra.discrete-fields" -> "ring-theory.division-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.11694168394216668 shape=circle style=filled width=0.11694168394216668] + "commutative-algebra.eisenstein-integers" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.eisenstein-integers" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.13289808409807344 shape=circle style=filled width=0.13289808409807344] + "commutative-algebra.euclidean-domains" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" -> "commutative-algebra.trivial-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] + 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[arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.euclidean-domains" -> "commutative-algebra.integral-domains" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07700228825802675 shape=circle style=filled width=0.07700228825802675] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "ring-theory.full-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06432675209026768 shape=circle style=filled width=0.06432675209026768] + "commutative-algebra.function-commutative-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-rings" -> "commutative-algebra.dependent-products-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06757856842230686 shape=circle style=filled width=0.06757856842230686] + "commutative-algebra.function-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.function-commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] + 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[arrowhead=none color="#3577BB10"] + "commutative-algebra.gaussian-integers" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.gaussian-integers" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.gaussian-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.gaussian-integers" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09069398819863565 shape=circle style=filled width=0.09069398819863565] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "category-theory.functors-large-precategories" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "ring-theory.groups-of-units-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.submonoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.category-of-abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.1060808838144246 shape=circle style=filled width=0.1060808838144246] + "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.invertible-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09907053327553424 shape=circle style=filled width=0.09907053327553424] + "commutative-algebra.homomorphisms-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-semirings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-semirings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-semirings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.homomorphisms-commutative-semirings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.08223128882139645 shape=circle style=filled width=0.08223128882139645] + "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] + "commutative-algebra.ideals-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-semirings" -> "commutative-algebra.subsets-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-commutative-semirings" -> "ring-theory.ideals-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "ring-theory.ideals-generated-by-subsets-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09410728805605297 shape=circle style=filled width=0.09410728805605297] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.multiples-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.12456821978060995 shape=circle style=filled width=0.12456821978060995] + "commutative-algebra.integral-domains" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.involutions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "commutative-algebra.trivial-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.embeddings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.binary-equivalences" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.binary-embeddings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.negation" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "lists.lists" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] + "commutative-algebra.integral-domains" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05985685194678195 shape=circle style=filled width=0.05985685194678195] + "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "foundation.intersections-subtypes" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "ring-theory.intersections-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09124869666223606 shape=circle style=filled width=0.09124869666223606] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.products-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.full-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.intersections-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.invertible-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09356952772180921 shape=circle style=filled width=0.09356952772180921] + "commutative-algebra.invertible-elements-commutative-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.invertible-elements-commutative-rings" -> "foundation.contractible-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.invertible-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.10738108802578482 shape=circle style=filled width=0.10738108802578482] + "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "ring-theory.isomorphisms-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.invertible-elements-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "group-theory.isomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07942179611987281 shape=circle style=filled width=0.07942179611987281] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "ring-theory.joins-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.products-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.11769441979464867 shape=circle style=filled width=0.11769441979464867] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "order-theory.large-suplattices" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.joins-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.products-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.intersections-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.local-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] + "commutative-algebra.local-commutative-rings" -> "ring-theory.local-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.local-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.local-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.maximal-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] + "commutative-algebra.multiples-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05964571600864011 shape=circle style=filled width=0.05964571600864011] + "commutative-algebra.multiples-of-elements-commutative-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.multiples-of-elements-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] + "commutative-algebra.multiples-of-elements-commutative-rings" -> "ring-theory.multiples-of-elements-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.multiples-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] + "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "ring-theory.nilpotent-elements-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.prime-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradicals-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] + "commutative-algebra.nilradicals-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradicals-commutative-semirings" -> "commutative-algebra.subsets-commutative-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradicals-commutative-semirings" -> "ring-theory.nilpotent-elements-semirings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.nilradicals-commutative-semirings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] + "commutative-algebra.poset-of-ideals-commutative-rings" -> "order-theory.large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-ideals-commutative-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-ideals-commutative-rings" -> "order-theory.large-preorders" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06960177486788897 shape=circle style=filled width=0.06960177486788897] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#3577BB10"] + "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.large-preorders" 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"commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] + "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] + "commutative-algebra.trivial-commutative-rings" -> "group-theory.trivial-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "foundation.negation" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "foundation.structure-identity-principle" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "ring-theory.trivial-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "foundation.contractible-types" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.trivial-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] + 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shape=circle style=filled width=0.05] + "commutative-algebra.zariski-topology" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.zariski-topology" -> "commutative-algebra.prime-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] + "commutative-algebra.zariski-topology" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] + "domain-theory.directed-complete-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.06625891564490792 shape=circle style=filled width=0.06625891564490792] + "domain-theory.directed-complete-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-complete-posets" -> "foundation.binary-relations" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-complete-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-complete-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-complete-posets" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] + "domain-theory.directed-families-posets" -> "foundation.conjunction" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "foundation.existential-quantification" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "foundation.universal-quantification" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "foundation.surjective-maps" [arrowhead=none color="#FCBFF510"] + "domain-theory.directed-families-posets" -> "foundation.inhabited-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.08758031277559175 shape=circle style=filled width=0.08758031277559175] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-complete-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.fixed-points-endofunctions" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.chains-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-continuous-maps-omega-complete-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.kleenes-fixed-point-theorem-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-continuous-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.iterating-functions" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.inhabited-chains-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.suplattices" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.bottom-elements-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.inflattices" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.inhabited-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.09649012813540153 shape=circle style=filled width=0.09649012813540153] + "domain-theory.kleenes-fixed-point-theorem-posets" -> "foundation.fixed-points-endofunctions" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-posets" -> "order-theory.chains-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.kleenes-fixed-point-theorem-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] + 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+ "domain-theory.omega-complete-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "foundation.binary-relations" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "order-theory.upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-complete-posets" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.10021004013899694 shape=circle style=filled width=0.10021004013899694] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "domain-theory.omega-complete-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.subtype-identity-principle" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.join-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.existential-quantification" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.raising-universe-levels" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.booleans" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "domain-theory.omega-continuous-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.evaluation-functions" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.homotopy-induction" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.surjective-maps" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.torsorial-type-families" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.09701170019522755 shape=circle style=filled width=0.09701170019522755] + "domain-theory.omega-continuous-maps-posets" -> 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-> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.evaluation-functions" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.homotopy-induction" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.surjective-maps" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> "foundation.torsorial-type-families" [arrowhead=none color="#FCBFF510"] + "domain-theory.omega-continuous-maps-posets" -> 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color="#FCBFF510"] + "domain-theory.reindexing-directed-families-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] + "domain-theory.reindexing-directed-families-posets" -> "foundation.inhabited-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.scott-continuous-maps-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.09957859062409573 shape=circle style=filled width=0.09957859062409573] + "domain-theory.scott-continuous-maps-posets" -> "foundation.small-types" [arrowhead=none color="#FCBFF510"] + "domain-theory.scott-continuous-maps-posets" -> "foundation.subtype-identity-principle" [arrowhead=none color="#FCBFF510"] + "domain-theory.scott-continuous-maps-posets" -> "foundation.existential-quantification" [arrowhead=none color="#FCBFF510"] + "domain-theory.scott-continuous-maps-posets" -> "foundation.raising-universe-levels" [arrowhead=none color="#FCBFF510"] + "domain-theory.scott-continuous-maps-posets" -> 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-> "foundation.binary-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "elementary-number-theory.nonzero-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "elementary-number-theory.nonnegative-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "elementary-number-theory.nonpositive-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "foundation.negation" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#4A612310"] + 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color="#4A612310"] + "elementary-number-theory.divisibility-modular-arithmetic" -> "foundation.binary-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-modular-arithmetic" -> "elementary-number-theory.modular-arithmetic" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-modular-arithmetic" -> "univalent-combinatorics.fibers-of-maps" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.11509311694321234 shape=circle style=filled width=0.11509311694321234] + "elementary-number-theory.divisibility-natural-numbers" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.binary-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.negation" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.negated-equality" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.propositional-maps" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-natural-numbers" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.divisibility-standard-finite-types" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" -> "univalent-combinatorics.decidable-dependent-pair-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" -> "foundation.binary-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.divisibility-standard-finite-types" -> "elementary-number-theory.modular-arithmetic-standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.09570244044334736 shape=circle style=filled width=0.09570244044334736] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.maybe" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.injective-maps" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.double-negation-stable-equality" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.double-negation" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "elementary-number-theory.conatural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.negation" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.retracts-of-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.sections" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.retractions" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "logic.double-negation-elimination" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.tight-apartness-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.torsorial-type-families" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-conatural-numbers" -> "foundation.coherently-invertible-maps" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] + "elementary-number-theory.equality-integers" -> "foundation.discrete-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.decidable-equality" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.set-truncations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-integers" -> "foundation.torsorial-type-families" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.06923831664020327 shape=circle style=filled width=0.06923831664020327] + "elementary-number-theory.equality-natural-numbers" -> "foundation-core.decidable-propositions" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.discrete-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.decidable-equality" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.set-truncations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.tight-apartness-relations" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-natural-numbers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] + "elementary-number-theory.equality-rational-numbers" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "elementary-number-theory.reduced-integer-fractions" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "foundation.torsorial-type-families" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "foundation.decidable-equality" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "elementary-number-theory.equality-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "elementary-number-theory.integer-fractions" [arrowhead=none color="#4A612310"] + "elementary-number-theory.equality-rational-numbers" -> "elementary-number-theory.positive-integers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclid-mullin-sequence" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.euclid-mullin-sequence" -> "elementary-number-theory.strong-induction-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclid-mullin-sequence" -> "elementary-number-theory.fundamental-theorem-of-arithmetic" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclid-mullin-sequence" -> "elementary-number-theory.products-of-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclid-mullin-sequence" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclid-mullin-sequence" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.congruence-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.euclidean-division-natural-numbers" -> "elementary-number-theory.modular-arithmetic-standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.eulers-totient-function" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.eulers-totient-function" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#4A612310"] + "elementary-number-theory.eulers-totient-function" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.eulers-totient-function" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.eulers-totient-function" -> "elementary-number-theory.relatively-prime-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.exponentiation-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.exponentiation-natural-numbers" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.exponentiation-natural-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.exponentiation-natural-numbers" -> "elementary-number-theory.products-of-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.exponentiation-natural-numbers" -> "commutative-algebra.powers-of-elements-commutative-semirings" [arrowhead=none color="#4A612310"] + "elementary-number-theory.exponentiation-natural-numbers" -> "elementary-number-theory.commutative-semiring-of-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.factorials" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.factorials" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.factorials" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.factorials" -> "elementary-number-theory.divisibility-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.factorials" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.factorials" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.falling-factorials" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.falling-factorials" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fermat-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.fermat-numbers" -> "elementary-number-theory.strong-induction-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fermat-numbers" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fermat-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fermat-numbers" -> "elementary-number-theory.products-of-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fermat-numbers" -> "elementary-number-theory.exponentiation-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fibonacci-sequence" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.07667391879499177 shape=circle style=filled width=0.07667391879499177] + "elementary-number-theory.fibonacci-sequence" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fibonacci-sequence" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fibonacci-sequence" -> "elementary-number-theory.divisibility-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fibonacci-sequence" -> "elementary-number-theory.greatest-common-divisor-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fibonacci-sequence" -> "elementary-number-theory.relatively-prime-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.field-of-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05 shape=circle style=filled width=0.05] + "elementary-number-theory.field-of-rational-numbers" -> "commutative-algebra.discrete-fields" [arrowhead=none color="#4A612310"] + "elementary-number-theory.field-of-rational-numbers" -> "ring-theory.division-rings" [arrowhead=none color="#4A612310"] + "elementary-number-theory.field-of-rational-numbers" -> "elementary-number-theory.multiplicative-group-of-rational-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.field-of-rational-numbers" -> "elementary-number-theory.ring-of-rational-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.field-of-rational-numbers" -> "elementary-number-theory.nonzero-rational-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.07667391879499177 shape=circle style=filled width=0.07667391879499177] + "elementary-number-theory.finitary-natural-numbers" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "elementary-number-theory.congruence-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "foundation.empty-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "foundation.injective-maps" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitary-natural-numbers" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitely-cyclic-maps" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.05705116998481125 shape=circle style=filled width=0.05705116998481125] + "elementary-number-theory.finitely-cyclic-maps" -> "foundation.iterating-functions" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitely-cyclic-maps" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.finitely-cyclic-maps" -> "elementary-number-theory.modular-arithmetic-standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" [label="" color="#FFFFFF00" fillcolor="#4A6123" height=0.16682358746764833 shape=circle style=filled width=0.16682358746764833] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "lists.concatenation-lists" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "finite-group-theory.permutations-standard-finite-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "lists.permutation-lists" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "lists.sort-by-insertion-lists" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "foundation.contractible-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "lists.predicates-on-lists" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.fundamental-theorem-of-arithmetic" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#4A612310"] + 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color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "foundation.decidable-types" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "foundation.negation" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#4A612310"] + "elementary-number-theory.squares-natural-numbers" -> "elementary-number-theory.decidable-types" [arrowhead=none color="#4A612310"] + 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"foundation.binary-embeddings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "ring-theory.division-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "lists.lists" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "foundation.unital-binary-operations" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "ring-theory.rings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-fields" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.12426402342964542 shape=circle style=filled width=0.12426402342964542] + "finite-algebra.finite-rings" -> "lists.concatenation-lists" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "univalent-combinatorics.dependent-function-types" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.involutions" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "group-theory.groups" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "group-theory.semigroups" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "finite-group-theory.finite-abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "group-theory.monoids" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.embeddings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "univalent-combinatorics.cartesian-product-types" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "ring-theory.semirings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.binary-equivalences" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.injective-maps" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.binary-embeddings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "lists.lists" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "finite-group-theory.finite-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "foundation.unital-binary-operations" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "ring-theory.rings" [arrowhead=none color="#524F8810"] + "finite-algebra.finite-rings" -> "finite-group-theory.finite-monoids" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.10820035616009187 shape=circle style=filled width=0.10820035616009187] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "commutative-algebra.homomorphisms-commutative-semirings" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-commutative-finite-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.101957295765424 shape=circle style=filled width=0.101957295765424] + "finite-algebra.homomorphisms-finite-rings" -> "finite-algebra.finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-finite-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-finite-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-finite-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#524F8810"] + "finite-algebra.homomorphisms-finite-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.08553989227683015 shape=circle style=filled width=0.08553989227683015] + "finite-algebra.products-commutative-finite-rings" -> "group-theory.semigroups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "group-theory.groups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "commutative-algebra.products-commutative-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "finite-algebra.products-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-commutative-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.07121438510526466 shape=circle style=filled width=0.07121438510526466] + "finite-algebra.products-finite-rings" -> "finite-algebra.finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "group-theory.semigroups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "group-theory.groups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "ring-theory.products-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "univalent-combinatorics.cartesian-product-types" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "ring-theory.rings" [arrowhead=none color="#524F8810"] + "finite-algebra.products-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.05 shape=circle style=filled width=0.05] + "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.dependent-products-commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.homomorphisms-commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.finite-fields" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "foundation.existential-quantification" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] + "finite-algebra.semisimple-commutative-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] + "finite-group-theory.abstract-quaternion-group" [label="" color="#FFFFFF00" fillcolor="#9A01E2" height=0.1540045765160535 shape=circle style=filled width=0.1540045765160535] + "finite-group-theory.abstract-quaternion-group" -> "group-theory.semigroups" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "group-theory.groups" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "foundation.decidable-types" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "foundation.decidable-equality" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "foundation.negation" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#9A01E210"] + "finite-group-theory.abstract-quaternion-group" -> "foundation.empty-types" 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"group-theory.symmetric-groups" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.mere-equivalences" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "finite-group-theory.delooping-sign-homomorphism" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.action-on-equivalences-type-families-over-subuniverses" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "group-theory.concrete-groups" [arrowhead=none color="#9A01E210"] + "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.equivalence-relations" [arrowhead=none color="#9A01E210"] + "finite-group-theory.concrete-quaternion-group" [label="" color="#FFFFFF00" 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+ "foundation-core.propositional-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.propositional-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation-core.propositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10749850860545447 shape=circle style=filled width=0.10749850860545447] + "foundation-core.propositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation-core.propositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.propositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.propositions" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.propositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" [label="" color="#FFFFFF00" 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"foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" -> "foundation-core.diagonal-maps-cartesian-products-of-types" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" -> "foundation.type-arithmetic-standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation-core.pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation-core.retractions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08253755166479786 shape=circle style=filled width=0.08253755166479786] + "foundation-core.retractions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation-core.retractions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07765486169039741 shape=circle style=filled width=0.07765486169039741] + "foundation-core.retracts-of-types" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" -> "foundation-core.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation-core.retracts-of-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation-core.sections" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07399452165296407 shape=circle style=filled width=0.07399452165296407] + "foundation-core.sections" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation-core.sections" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.sets" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07667391879499177 shape=circle style=filled width=0.07667391879499177] + "foundation-core.sets" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation-core.sets" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation-core.small-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09464199285965737 shape=circle style=filled width=0.09464199285965737] + "foundation-core.small-types" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.coherently-invertible-maps" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation.mere-equivalences" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation-core.small-types" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09740104637608157 shape=circle style=filled width=0.09740104637608157] + "foundation-core.subtypes" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation-core.torsorial-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] + "foundation-core.torsorial-type-families" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.transport-along-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] + "foundation-core.truncated-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08700221858486124 shape=circle style=filled width=0.08700221858486124] + "foundation-core.truncated-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation.equality-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10584276705216185 shape=circle style=filled width=0.10584276705216185] + "foundation-core.truncated-types" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.retracts-of-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation-core.truncated-types" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.truncation-levels" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation-core.type-theoretic-principle-of-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07050222336024897 shape=circle style=filled width=0.07050222336024897] + "foundation-core.type-theoretic-principle-of-choice" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.univalence" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] + "foundation-core.univalence" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation-core.univalence" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07584677573504928 shape=circle style=filled width=0.07584677573504928] + "foundation-core.universal-property-pullbacks" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07296438524291976 shape=circle style=filled width=0.07296438524291976] + "foundation-core.universal-property-truncation" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.universal-property-truncation" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation-core.whiskering-homotopies-concatenation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] + "foundation-core.whiskering-homotopies-concatenation" -> "foundation.whiskering-operations" [arrowhead=none color="#28453010"] + "foundation-core.whiskering-homotopies-concatenation" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] + "foundation-core.whiskering-homotopies-concatenation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.whiskering-identifications-concatenation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09207449355456987 shape=circle style=filled width=0.09207449355456987] + "foundation-core.whiskering-identifications-concatenation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation-core.whiskering-identifications-concatenation" -> "foundation.whiskering-operations" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08068253834177291 shape=circle style=filled width=0.08068253834177291] + "foundation.0-connected-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.constant-maps" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.universal-property-unit-type" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.set-truncations" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.fiber-inclusions" [arrowhead=none color="#28453010"] + "foundation.0-connected-types" -> "foundation.functoriality-set-truncation" [arrowhead=none color="#28453010"] + "foundation.0-images-of-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.0-images-of-maps" -> "foundation.truncation-images-of-maps" [arrowhead=none color="#28453010"] + "foundation.0-images-of-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.0-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0631390791325705 shape=circle style=filled width=0.0631390791325705] + "foundation.0-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.0-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.0-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.0-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.0-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.0-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.1-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] + "foundation.1-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation-core.1-types" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.1-types" -> "foundation.truncated-types" [arrowhead=none color="#28453010"] + "foundation.2-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.2-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.2-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions-out-of-subuniverses" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.equivalence-induction" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] + "foundation.action-on-equivalences-functions" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-functions" -> "foundation.equivalence-induction" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation-core.univalence" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families-over-subuniverses" -> "foundation.equivalence-induction" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06887294038719267 shape=circle style=filled width=0.06887294038719267] + "foundation.action-on-equivalences-type-families" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation.whiskering-higher-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation.action-on-equivalences-functions" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-equivalences-type-families" -> "foundation.equivalence-induction" [arrowhead=none color="#28453010"] + "foundation.action-on-higher-identifications-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07014343109049616 shape=circle style=filled width=0.07014343109049616] + "foundation.action-on-higher-identifications-functions" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-higher-identifications-functions" -> "foundation-core.commuting-squares-of-identifications" [arrowhead=none color="#28453010"] + "foundation.action-on-higher-identifications-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.action-on-higher-identifications-functions" -> "foundation.path-algebra" [arrowhead=none color="#28453010"] + "foundation.action-on-homotopies-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] + "foundation.action-on-homotopies-functions" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.action-on-homotopies-functions" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] + "foundation.action-on-homotopies-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.action-on-homotopies-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.action-on-homotopies-functions" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.action-on-identifications-binary-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.action-on-identifications-binary-dependent-functions" -> "foundation.binary-dependent-identifications" [arrowhead=none color="#28453010"] + "foundation.action-on-identifications-binary-dependent-functions" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.action-on-identifications-binary-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07174386737769174 shape=circle style=filled width=0.07174386737769174] + "foundation.action-on-identifications-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.action-on-identifications-dependent-functions" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07551338170027617 shape=circle style=filled width=0.07551338170027617] + "foundation.apartness-relations" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation.disjunction" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation.universal-quantification" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation-core.negation" [arrowhead=none color="#28453010"] + "foundation.apartness-relations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07534613148009645 shape=circle style=filled width=0.07534613148009645] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.coproduct-decompositions" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07534613148009645 shape=circle style=filled width=0.07534613148009645] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.pi-decompositions" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.product-decompositions" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.coproduct-decompositions" [arrowhead=none color="#28453010"] + "foundation.automorphisms" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.automorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] + "foundation.automorphisms" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.061108350049340496 shape=circle style=filled width=0.061108350049340496] + "foundation.axiom-of-choice" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.split-surjective-maps" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.projective-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "foundation.sections" [arrowhead=none color="#28453010"] + "foundation.axiom-of-choice" -> "univalent-combinatorics.counting" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06606824211104302 shape=circle style=filled width=0.06606824211104302] + "foundation.axiom-of-countable-choice" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.embeddings" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.maybe" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.axiom-of-dependent-choice" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.decidable-equality" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "univalent-combinatorics.classical-finite-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "set-theory.countable-sets" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-countable-choice" -> "foundation.axiom-of-choice" [arrowhead=none color="#28453010"] + "foundation.axiom-of-dependent-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.axiom-of-dependent-choice" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] + "foundation.axiom-of-dependent-choice" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.axiom-of-dependent-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.axiom-of-dependent-choice" -> "foundation.axiom-of-choice" [arrowhead=none color="#28453010"] + "foundation.bands" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.bands" -> "foundation.set-truncations" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07313708225430403 shape=circle style=filled width=0.07313708225430403] + "foundation.base-changes-span-diagrams" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" -> "foundation.cartesian-morphisms-span-diagrams" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" -> "foundation.cartesian-morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.base-changes-span-diagrams" -> "foundation.morphisms-span-diagrams" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.bicomposition-functions" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation.postcomposition-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.bicomposition-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.binary-dependent-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-dependent-identifications" -> "foundation.binary-transport" [arrowhead=none color="#28453010"] + "foundation.binary-embeddings" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-embeddings" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.binary-embeddings" -> "foundation.binary-equivalences" [arrowhead=none color="#28453010"] + "foundation.binary-embeddings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#28453010"] + "foundation.binary-equivalences-unordered-pairs-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.products-unordered-pairs-of-types" [arrowhead=none color="#28453010"] + "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.binary-operations-unordered-pairs-of-types" [arrowhead=none color="#28453010"] + "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.unordered-pairs" [arrowhead=none color="#28453010"] + "foundation.binary-equivalences" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-equivalences" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10993537362971544 shape=circle style=filled 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"foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation.binary-homotopies" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.binary-functoriality-set-quotients" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#28453010"] + "foundation.binary-homotopies" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-homotopies" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.binary-homotopies" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.binary-homotopies" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.binary-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.binary-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.binary-operations-unordered-pairs-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.binary-operations-unordered-pairs-of-types" -> "foundation.products-unordered-pairs-of-types" [arrowhead=none color="#28453010"] + "foundation.binary-operations-unordered-pairs-of-types" -> "foundation.unordered-pairs" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06131444962281207 shape=circle style=filled width=0.06131444962281207] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.binary-relations-with-extensions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05857862241641752 shape=circle style=filled width=0.05857862241641752] + "foundation.binary-relations-with-extensions" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + 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height=0.05 shape=circle style=filled width=0.05] + "foundation.commuting-triangles-of-morphisms-arrows" -> "foundation.homotopies-morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.commuting-triangles-of-morphisms-arrows" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.complements-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.complements-subtypes" -> "foundation.decidable-subtypes" [arrowhead=none color="#28453010"] + "foundation.complements-subtypes" -> "logic.double-negation-stable-subtypes" [arrowhead=none color="#28453010"] + "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#28453010"] + "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#28453010"] + "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-large-posets" 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"foundation.connected-components-universes" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.connected-components-universes" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.connected-components-universes" -> "foundation.mere-equivalences" [arrowhead=none color="#28453010"] + "foundation.connected-components-universes" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.connected-components-universes" -> "foundation.0-connected-types" [arrowhead=none color="#28453010"] + "foundation.connected-components-universes" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.connected-components" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] + "foundation.connected-components" -> "higher-group-theory.higher-groups" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation.0-connected-types" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.connected-components" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] + "foundation.connected-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.12180310601880573 shape=circle style=filled width=0.12180310601880573] + "foundation.connected-maps" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.precomposition-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.universal-property-family-of-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.connected-types" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.truncated-types" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.iterated-successors-truncation-levels" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.truncations" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.connected-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.connected-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08299482691834507 shape=circle style=filled width=0.08299482691834507] + "foundation.connected-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.retracts-of-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.functoriality-truncation" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.truncations" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.diagonal-maps-of-types" [arrowhead=none color="#28453010"] + "foundation.connected-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07226947050238228 shape=circle style=filled width=0.07226947050238228] + "foundation.constant-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.faithful-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.retracts-of-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.1-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.retracts-of-types" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.type-arithmetic-unit-type" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.action-on-homotopies-functions" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.0-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.constant-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.constant-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.constant-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] + "foundation.constant-span-diagrams" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.constant-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] + "foundation.constant-type-families" -> "foundation-core.commuting-squares-of-identifications" [arrowhead=none color="#28453010"] + "foundation.constant-type-families" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] + "foundation.constant-type-families" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.continuations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07068093650719452 shape=circle style=filled width=0.07068093650719452] + "foundation.continuations" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.type-arithmetic-unit-type" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "orthogonal-factorization-systems.extensions-maps" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "orthogonal-factorization-systems.types-local-at-maps" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.universal-property-empty-type" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "orthogonal-factorization-systems.modal-operators" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.evaluation-functions" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "orthogonal-factorization-systems.uniquely-eliminating-modalities" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.type-arithmetic-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.universal-property-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.continuations" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05943383002455521 shape=circle style=filled width=0.05943383002455521] + "foundation.contractible-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.contractible-maps" -> "foundation.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.contractible-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07244382412249044 shape=circle style=filled width=0.07244382412249044] + "foundation.contractible-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.contractible-types" -> "foundation.diagonal-maps-of-types" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] + "foundation.copartial-elements" -> "synthetic-homotopy-theory.joins-of-types" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" -> "foundation.partial-elements" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" -> "foundation.negation" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" -> "orthogonal-factorization-systems.closed-modalities" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.copartial-elements" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.copartial-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0690558701659274 shape=circle style=filled width=0.0690558701659274] + "foundation.copartial-functions" -> "foundation.partial-functions" [arrowhead=none color="#28453010"] + "foundation.copartial-functions" -> "foundation.copartial-elements" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.11287958111098491 shape=circle style=filled width=0.11287958111098491] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.equivalence-extensionality" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.1479037715942641 shape=circle style=filled width=0.1479037715942641] + "foundation.coproduct-decompositions" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.coproduct-decompositions-subuniverse" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coproduct-decompositions" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08021208221262416 shape=circle style=filled width=0.08021208221262416] + "foundation.coproducts-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation.equality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.coproducts-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.coslice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.052921383526080924 shape=circle style=filled width=0.052921383526080924] + "foundation.coslice" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.coslice" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.coslice" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.coslice" -> "foundation.commuting-triangles-of-homotopies" [arrowhead=none color="#28453010"] + "foundation.cospan-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.cospan-diagrams" -> "foundation.cospans" [arrowhead=none color="#28453010"] + "foundation.cospans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05023075432006429 shape=circle style=filled width=0.05023075432006429] + "foundation.cospans" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.cospans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + 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-> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.dependent-epimorphisms" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.dependent-epimorphisms" -> "foundation-core.precomposition-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.dependent-epimorphisms" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.dependent-epimorphisms" -> "foundation.epimorphisms" [arrowhead=none color="#28453010"] + "foundation.dependent-function-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.dependent-function-types" -> "foundation.universal-property-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.dependent-function-types" -> "foundation.terminal-spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.dependent-function-types" -> "foundation.type-arithmetic-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.dependent-function-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.dependent-homotopies" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.dependent-homotopies" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] + "foundation.dependent-homotopies" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08758031277559175 shape=circle style=filled width=0.08758031277559175] + "foundation.dependent-identifications" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" -> "foundation.transport-along-higher-identifications" [arrowhead=none color="#28453010"] + "foundation.dependent-identifications" -> "foundation.strictly-right-unital-concatenation-identifications" [arrowhead=none color="#28453010"] + "foundation.dependent-inverse-sequential-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07296438524291976 shape=circle style=filled width=0.07296438524291976] + "foundation.dependent-inverse-sequential-diagrams" -> "foundation.iterating-families-of-maps" [arrowhead=none color="#28453010"] + "foundation.dependent-inverse-sequential-diagrams" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + 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"foundation.dependent-products-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.dependent-products-pullbacks" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.dependent-products-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.dependent-sums-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09881552504494161 shape=circle style=filled width=0.09881552504494161] + "foundation.dependent-sums-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.dependent-sums-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.dependent-telescopes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05073057513131416 shape=circle style=filled 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color="#28453010"] + "foundation.descent-coproduct-types" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.descent-coproduct-types" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.descent-coproduct-types" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] + "foundation.descent-coproduct-types" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.descent-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.descent-dependent-pair-types" -> "foundation.functoriality-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.descent-dependent-pair-types" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.descent-dependent-pair-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.descent-dependent-pair-types" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.descent-dependent-pair-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.descent-empty-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.descent-empty-types" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.descent-empty-types" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.descent-empty-types" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.descent-equivalences" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.descent-equivalences" -> "foundation.functoriality-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.descent-equivalences" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.descent-equivalences" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.descent-equivalences" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.diaconescus-theorem" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.diaconescus-theorem" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.diaconescus-theorem" -> "foundation.booleans" [arrowhead=none color="#28453010"] + "foundation.diaconescus-theorem" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.diaconescus-theorem" -> "synthetic-homotopy-theory.suspensions-of-types" [arrowhead=none color="#28453010"] + "foundation.diaconescus-theorem" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] + 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[arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation.faithful-maps" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation.0-maps" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-cartesian-products-of-types" -> 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[arrowhead=none color="#28453010"] + "foundation.diagonal-maps-of-types" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.diagonal-maps-of-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.diagonal-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.diagonal-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0561596906103775 shape=circle style=filled width=0.0561596906103775] + "foundation.diagonals-of-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation.equality-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.diagonals-of-morphisms-arrows" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.discrete-binary-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.discrete-binary-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.discrete-binary-relations" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.discrete-reflexive-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.discrete-reflexive-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.discrete-reflexive-relations" -> "foundation.reflexive-relations" [arrowhead=none color="#28453010"] + "foundation.discrete-reflexive-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.discrete-reflexive-relations" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.discrete-reflexive-relations" -> "foundation.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05433286809186783 shape=circle style=filled width=0.05433286809186783] + "foundation.discrete-relaxed-sigma-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.discrete-relaxed-sigma-decompositions" -> 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"foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07433472814399888 shape=circle style=filled width=0.07433472814399888] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.morphisms-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.commuting-squares-of-homotopies" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.homotopies-morphisms-cospan-diagrams" -> "foundation.cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.homotopy-algebra" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.055481681563074876 shape=circle style=filled width=0.055481681563074876] + "foundation.homotopy-algebra" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.homotopy-algebra" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.homotopy-algebra" -> "foundation-core.whiskering-homotopies-concatenation" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06757856842230686 shape=circle style=filled width=0.06757856842230686] + "foundation.homotopy-induction" -> "foundation.universal-property-identity-systems" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation.identity-systems" [arrowhead=none color="#28453010"] + "foundation.homotopy-induction" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.homotopy-preorder-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.homotopy-preorder-of-types" -> "order-theory.preorders" [arrowhead=none color="#28453010"] + "foundation.homotopy-preorder-of-types" -> "foundation.mere-functions" [arrowhead=none color="#28453010"] + "foundation.homotopy-preorder-of-types" -> "order-theory.large-preorders" [arrowhead=none color="#28453010"] + "foundation.homotopy-preorder-of-types" -> "order-theory.posets" [arrowhead=none color="#28453010"] + "foundation.homotopy-preorder-of-types" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + 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"foundation.equivalences-arrows" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.spans-of-spans" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.horizontal-composition-spans-of-spans" -> "foundation.type-arithmetic-standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] + "foundation.idempotent-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" -> "foundation.homotopy-algebra" [arrowhead=none color="#28453010"] + "foundation.idempotent-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.identity-systems" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.057710742994894 shape=circle style=filled width=0.057710742994894] + "foundation.identity-systems" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.identity-systems" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.identity-truncated-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.identity-truncated-types" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.identity-truncated-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.identity-truncated-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08284268228643028 shape=circle style=filled width=0.08284268228643028] + "foundation.images-subtypes" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.full-subtypes" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.powersets" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#28453010"] + "foundation.images-subtypes" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.images" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08021208221262416 shape=circle style=filled width=0.08021208221262416] + "foundation.images" -> "foundation.slice" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation.embeddings" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.images" -> "foundation-core.1-types" [arrowhead=none color="#28453010"] + 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[arrowhead=none color="#28453010"] + "foundation.impredicative-encodings" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.impredicative-encodings" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.impredicative-universes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.impredicative-universes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.impredicative-universes" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] + "foundation.induction-principle-propositional-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.induction-principle-propositional-truncation" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.induction-principle-propositional-truncation" -> "foundation-core.propositions" 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color="#28453010"] + "foundation.inequality-booleans" -> "foundation.decidable-propositions" [arrowhead=none color="#28453010"] + "foundation.inequality-booleans" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.inequality-booleans" -> "foundation.logical-operations-booleans" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0832982825080884 shape=circle style=filled width=0.0832982825080884] + "foundation.inequality-truncation-levels" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "order-theory.preorders" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "order-theory.decidable-total-orders" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "order-theory.decidable-posets" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "order-theory.posets" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.disjunction" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "order-theory.total-orders" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.equality-truncation-levels" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.negation" [arrowhead=none color="#28453010"] + "foundation.inequality-truncation-levels" -> "foundation.empty-types" [arrowhead=none color="#28453010"] 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[arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation.infinity-connected-types" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation.connected-maps" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation.connected-types" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.infinity-connected-types" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation.functoriality-truncation" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation.connected-types" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation.truncations" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.infinity-connected-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.inhabited-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0629389547650211 shape=circle style=filled width=0.0629389547650211] + "foundation.inhabited-subtypes" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.inhabited-subtypes" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.inhabited-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.inhabited-subtypes" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08130557877817587 shape=circle style=filled width=0.08130557877817587] + "foundation.inhabited-types" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.inhabited-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.injective-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06131444962281207 shape=circle style=filled width=0.06131444962281207] + "foundation.injective-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.negation" [arrowhead=none color="#28453010"] + "foundation.injective-maps" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.interchange-law" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.intersections-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05220133115091674 shape=circle style=filled width=0.05220133115091674] + "foundation.intersections-subtypes" -> "foundation.decidable-subtypes" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation.powersets" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation-core.decidable-propositions" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation.conjunction" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.intersections-subtypes" -> "foundation.inhabited-subtypes" [arrowhead=none color="#28453010"] + "foundation.inverse-sequential-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0587935905605436 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"foundation.morphisms-arrows" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09543843320812216 shape=circle style=filled width=0.09543843320812216] + "foundation.morphisms-arrows" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.morphisms-arrows" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-binary-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.morphisms-binary-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.morphisms-binary-relations" -> "foundation.binary-homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-coalgebras-maybe" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.morphisms-coalgebras-maybe" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-coalgebras-maybe" -> "trees.polynomial-endofunctors" [arrowhead=none color="#28453010"] + "foundation.morphisms-coalgebras-maybe" -> "foundation.coalgebras-maybe" [arrowhead=none color="#28453010"] + "foundation.morphisms-coalgebras-maybe" -> "foundation.maybe" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospan-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0647177997777583 shape=circle style=filled width=0.0647177997777583] + "foundation.morphisms-cospan-diagrams" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospan-diagrams" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospan-diagrams" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospan-diagrams" -> "foundation.cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.morphisms-cospans" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-cospans" -> "foundation.cospans" [arrowhead=none color="#28453010"] + "foundation.morphisms-double-arrows" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07103701400766586 shape=circle style=filled width=0.07103701400766586] + "foundation.morphisms-double-arrows" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-double-arrows" -> "foundation.double-arrows" [arrowhead=none color="#28453010"] + "foundation.morphisms-double-arrows" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07584677573504928 shape=circle style=filled width=0.07584677573504928] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.dependent-inverse-sequential-diagrams" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.binary-homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.morphisms-inverse-sequential-diagrams" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06776499241351715 shape=circle style=filled width=0.06776499241351715] + "foundation.morphisms-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] + "foundation.morphisms-span-diagrams" -> "foundation.operations-spans" [arrowhead=none color="#28453010"] + "foundation.morphisms-span-diagrams" -> "foundation.morphisms-spans" [arrowhead=none color="#28453010"] + "foundation.morphisms-span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.morphisms-span-diagrams" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07279127850973344 shape=circle style=filled width=0.07279127850973344] + "foundation.morphisms-spans-families-of-types" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.commuting-triangles-of-homotopies" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans-families-of-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.morphisms-spans" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans" -> "foundation-core.operations-spans" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.morphisms-spans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.morphisms-twisted-arrows" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.morphisms-twisted-arrows" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.multisubsets" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multisubsets" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.multisubsets" -> "foundation.negated-equality" [arrowhead=none color="#28453010"] + "foundation.multisubsets" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.multisubsets" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.multisubsets" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-correspondences" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multivariable-correspondences" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-decidable-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multivariable-decidable-relations" -> "foundation.decidable-subtypes" [arrowhead=none color="#28453010"] + "foundation.multivariable-decidable-relations" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-decidable-relations" -> "foundation.multivariable-relations" [arrowhead=none color="#28453010"] + "foundation.multivariable-decidable-relations" -> "foundation.multivariable-correspondences" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multivariable-functoriality-set-quotients" -> "foundation.finite-sequences-set-quotients" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "foundation.set-quotients" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "lists.finite-sequences" [arrowhead=none color="#28453010"] + "foundation.multivariable-functoriality-set-quotients" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07716594899155892 shape=circle style=filled width=0.07716594899155892] + "foundation.multivariable-homotopies" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation.implicit-function-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation.telescopes" [arrowhead=none color="#28453010"] + "foundation.multivariable-homotopies" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "foundation.multivariable-operations" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "lists.tuples" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "lists.finite-sequences" [arrowhead=none color="#28453010"] + "foundation.multivariable-operations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multivariable-relations" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.multivariable-relations" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] + "foundation.multivariable-relations" -> "foundation.multivariable-correspondences" [arrowhead=none color="#28453010"] + "foundation.multivariable-sections" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.multivariable-sections" -> "foundation.multivariable-homotopies" [arrowhead=none color="#28453010"] + "foundation.multivariable-sections" -> "foundation.telescopes" [arrowhead=none color="#28453010"] + "foundation.multivariable-sections" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] + "foundation.negated-equality" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] + "foundation.negated-equality" -> "foundation.negation" [arrowhead=none color="#28453010"] + "foundation.negated-equality" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] + "foundation.negated-equality" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.negated-equality" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.negation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] + "foundation.negation" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.negation" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.negation" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.negation" -> "foundation-core.negation" [arrowhead=none color="#28453010"] + "foundation.noncontractible-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.056383881883468684 shape=circle style=filled width=0.056383881883468684] + "foundation.noncontractible-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.noncontractible-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.noncontractible-types" -> "foundation-core.negation" [arrowhead=none color="#28453010"] + "foundation.noncontractible-types" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.noncontractible-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05922118594381655 shape=circle style=filled width=0.05922118594381655] + "foundation.noninjective-maps" -> "foundation.repetitions-of-values" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation.negation" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.noninjective-maps" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09740104637608157 shape=circle style=filled width=0.09740104637608157] + "foundation.null-homotopic-maps" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.constant-maps" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.universal-property-empty-type" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.weakly-constant-maps" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.coherently-constant-maps" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.null-homotopic-maps" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.operations-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06510649876675342 shape=circle style=filled width=0.06510649876675342] + "foundation.operations-span-diagrams" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.operations-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] + "foundation.operations-span-diagrams" -> "foundation.operations-spans" [arrowhead=none color="#28453010"] + "foundation.operations-span-diagrams" -> "foundation.equivalences-arrows" [arrowhead=none color="#28453010"] + "foundation.operations-span-diagrams" -> "foundation-core.operations-span-diagrams" [arrowhead=none color="#28453010"] + "foundation.operations-spans-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.operations-spans-families-of-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.operations-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] + "foundation.operations-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.operations-spans" -> "foundation-core.operations-spans" [arrowhead=none color="#28453010"] + "foundation.operations-spans" -> "foundation.equivalences-arrows" [arrowhead=none color="#28453010"] + "foundation.operations-spans" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.opposite-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.opposite-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.pairs-of-distinct-elements" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07156780854205468 shape=circle style=filled width=0.07156780854205468] + "foundation.pairs-of-distinct-elements" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.pairs-of-distinct-elements" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.pairs-of-distinct-elements" -> "foundation.subtype-identity-principle" [arrowhead=none 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"foundation.precomposition-functions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.precomposition-functions" -> "foundation.sections" [arrowhead=none color="#28453010"] + "foundation.precomposition-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.precomposition-type-families" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.precomposition-type-families" -> "foundation.transport-along-homotopies" [arrowhead=none color="#28453010"] + "foundation.precomposition-type-families" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.precomposition-type-families" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.preunivalence" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] + "foundation.preunivalence" -> "foundation.embeddings" [arrowhead=none color="#28453010"] + "foundation.preunivalence" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.preunivalence" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.preunivalent-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" 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+ "foundation.product-decompositions-subuniverse" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.product-decompositions-subuniverse" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.product-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle 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color="#28453010"] + "foundation.products-pullbacks" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.products-pullbacks" -> 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[arrowhead=none color="#28453010"] + "foundation.projective-types" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.projective-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.projective-types" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.proper-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.proper-subtypes" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.proper-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.proper-subtypes" -> "foundation.complements-subtypes" [arrowhead=none color="#28453010"] + "foundation.proper-subtypes" -> "foundation.inhabited-subtypes" [arrowhead=none color="#28453010"] + "foundation.propositional-extensionality" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06923831664020327 shape=circle style=filled 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color="#28453010"] + "foundation.set-presented-types" -> "foundation.empty-types" [arrowhead=none color="#28453010"] + "foundation.set-quotients" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.12211343290652059 shape=circle style=filled width=0.12211343290652059] + "foundation.set-quotients" -> "foundation.slice" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.uniqueness-set-quotients" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.equivalence-classes" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#28453010"] + 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[arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.universal-property-image" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.set-quotients" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.set-truncations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.119819039333119 shape=circle style=filled width=0.119819039333119] + "foundation.set-truncations" -> "foundation.slice" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.equality-coproduct-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.truncations" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.universal-property-image" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.universal-property-set-truncation" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.uniqueness-set-truncations" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] + "foundation.set-truncations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.sigma-closed-subuniverses" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.sigma-closed-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.sigma-decomposition-subuniverse" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05964571600864011 shape=circle style=filled width=0.05964571600864011] + "foundation.sigma-decomposition-subuniverse" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.sigma-decomposition-subuniverse" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.sigma-decomposition-subuniverse" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] + "foundation.sigma-decomposition-subuniverse" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.sigma-decomposition-subuniverse" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.1574876341815475 shape=circle style=filled width=0.1574876341815475] + "foundation.sigma-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.sigma-decompositions" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] + "foundation.singleton-induction" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] + "foundation.singleton-induction" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] + "foundation.singleton-induction" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.singleton-induction" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.singleton-induction" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08284268228643028 shape=circle style=filled width=0.08284268228643028] + "foundation.singleton-subtypes" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.singleton-induction" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.connected-components" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.images-subtypes" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.inhabited-subtypes" [arrowhead=none color="#28453010"] + "foundation.singleton-subtypes" -> "foundation.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.slice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09817510660004068 shape=circle style=filled width=0.09817510660004068] + "foundation.slice" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.commuting-triangles-of-homotopies" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.slice" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.slice" -> "trees.polynomial-endofunctors" [arrowhead=none color="#28453010"] + "foundation.small-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.small-maps" -> "foundation.retracts-of-maps" [arrowhead=none color="#28453010"] + "foundation.small-maps" -> "foundation.split-idempotent-maps" [arrowhead=none color="#28453010"] + "foundation.small-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.small-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.small-maps" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] + "foundation.small-maps" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] + "foundation.small-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.small-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.replacement" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.uniqueness-image" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.universal-property-image" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] + "foundation.small-types" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] + "foundation.small-universes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.small-universes" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.small-universes" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] + "foundation.sorial-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.sorial-type-families" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] + "foundation.span-diagrams-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.span-diagrams-families-of-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05985685194678195 shape=circle style=filled width=0.05985685194678195] + "foundation.span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] + "foundation.span-diagrams" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.spans-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.spans-of-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] + "foundation.spans-of-spans" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.spans-of-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] + "foundation.spans-of-spans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.spans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.17530461293723326 shape=circle style=filled width=0.17530461293723326] + "foundation.split-idempotent-maps" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.commuting-squares-of-homotopies" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.retracts-of-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.sequential-limits" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.homotopy-algebra" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.fixed-points-endofunctions" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.quasicoherently-idempotent-maps" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.path-cosplit-maps" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.idempotent-maps" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation.weakly-constant-maps" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.split-idempotent-maps" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.054564565808626536 shape=circle style=filled width=0.054564565808626536] + "foundation.split-surjective-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.split-surjective-maps" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.standard-apartness-relations" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation.negated-equality" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation.tight-apartness-relations" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation.law-of-excluded-middle" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation-core.negation" [arrowhead=none color="#28453010"] + "foundation.standard-apartness-relations" -> "foundation.apartness-relations" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10046150864012858 shape=circle style=filled width=0.10046150864012858] + "foundation.standard-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.diagonal-maps-cartesian-products-of-types" [arrowhead=none color="#28453010"] + "foundation.standard-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.standard-ternary-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.standard-ternary-pullbacks" -> 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"foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-cartesian-product-types" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-cartesian-product-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.universal-property-cartesian-product-types" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-contractible-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06996334496256991 shape=circle style=filled width=0.06996334496256991] + "foundation.universal-property-contractible-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-contractible-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-contractible-types" -> "foundation.singleton-induction" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05023075432006429 shape=circle style=filled width=0.05023075432006429] + "foundation.universal-property-coproduct-types" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-coproduct-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0561596906103775 shape=circle style=filled width=0.0561596906103775] + "foundation.universal-property-dependent-function-types" -> "foundation.terminal-spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-function-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05073057513131416 shape=circle style=filled width=0.05073057513131416] + "foundation.universal-property-dependent-pair-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-pair-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-pair-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.universal-property-dependent-pair-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.universal-property-empty-type" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.052442447127525396 shape=circle style=filled width=0.052442447127525396] + "foundation.universal-property-empty-type" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-empty-type" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-empty-type" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-equivalences" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05433286809186783 shape=circle style=filled width=0.05433286809186783] + "foundation.universal-property-equivalences" -> "foundation.precomposition-functions-into-subuniverses" [arrowhead=none color="#28453010"] + "foundation.universal-property-equivalences" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-equivalences" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10452342886887278 shape=circle style=filled width=0.10452342886887278] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.precomposition-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "orthogonal-factorization-systems.lifts-families-of-elements" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "orthogonal-factorization-systems.extensions-double-lifts-families-of-elements" [arrowhead=none color="#28453010"] + "foundation.universal-property-family-of-fibers-of-maps" -> "foundation.diagonal-maps-of-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.060276905184077155 shape=circle style=filled width=0.060276905184077155] + "foundation.universal-property-fiber-products" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-fiber-products" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-systems" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05220133115091674 shape=circle style=filled width=0.05220133115091674] + "foundation.universal-property-identity-systems" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-systems" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-systems" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-systems" -> "foundation.identity-systems" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-systems" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09329948523165156 shape=circle style=filled width=0.09329948523165156] + "foundation.universal-property-identity-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.embeddings" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.full-subtypes" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.preunivalence" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.univalence" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-identity-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09316417046104979 shape=circle style=filled width=0.09316417046104979] + "foundation.universal-property-image" -> "foundation.slice" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.embeddings" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.universal-property-family-of-fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.sections" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-image" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-maybe" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] + "foundation.universal-property-maybe" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-maybe" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-maybe" -> "foundation.maybe" [arrowhead=none color="#28453010"] + "foundation.universal-property-maybe" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06432675209026768 shape=circle style=filled width=0.06432675209026768] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation.weakly-constant-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation-into-sets" -> "foundation-core.sets" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09596572138218783 shape=circle style=filled width=0.09596572138218783] + "foundation.universal-property-propositional-truncation" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.precomposition-dependent-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation.precomposition-functions-into-subuniverses" [arrowhead=none color="#28453010"] + "foundation.universal-property-propositional-truncation" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] + "foundation.universal-property-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] + "foundation.universal-property-pullbacks" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-pullbacks" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.universal-property-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08192388105819126 shape=circle style=filled width=0.08192388105819126] + "foundation.universal-property-sequential-limits" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation.cones-over-inverse-sequential-diagrams" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] + "foundation.universal-property-sequential-limits" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.14747667347018004 shape=circle style=filled width=0.14747667347018004] + "foundation.universal-property-set-quotients" -> "foundation-core.univalence" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.propositional-extensionality" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.epimorphisms-with-respect-to-sets" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.equivalence-classes" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.small-types" [arrowhead=none 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[arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.images" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-quotients" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] + "foundation.universal-property-set-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0760129244023573 shape=circle style=filled width=0.0760129244023573] + "foundation.universal-property-set-truncation" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] + 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[arrowhead=none color="#28453010"] + "foundation.yoneda-identity-types" -> "foundation.strictly-right-unital-concatenation-identifications" [arrowhead=none color="#28453010"] + "globular-types.base-change-dependent-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.base-change-dependent-globular-types" -> "globular-types.dependent-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-globular-types" -> "globular-types.globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05479528381785756 shape=circle style=filled width=0.05479528381785756] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.dependent-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.base-change-dependent-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.reflexive-globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.dependent-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.base-change-dependent-reflexive-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.binary-dependent-globular-types" -> "globular-types.points-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-reflexive-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.0789438271083925 shape=circle style=filled width=0.0789438271083925] + "globular-types.binary-dependent-reflexive-globular-types" -> "globular-types.binary-dependent-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-reflexive-globular-types" -> "globular-types.points-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-dependent-reflexive-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-globular-maps" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.binary-globular-maps" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.binary-globular-maps" -> "globular-types.globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.colax-reflexive-globular-maps" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.07382383048755557 shape=circle style=filled width=0.07382383048755557] + "globular-types.colax-reflexive-globular-maps" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.colax-reflexive-globular-maps" -> "globular-types.globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.colax-transitive-globular-maps" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.07732926335200342 shape=circle style=filled width=0.07732926335200342] + "globular-types.colax-transitive-globular-maps" -> "globular-types.transitive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.colax-transitive-globular-maps" -> "globular-types.globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.composition-structure-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.composition-structure-globular-types" -> "globular-types.binary-globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.composition-structure-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.constant-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.constant-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.dependent-globular-types" -> "globular-types.points-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-reflexive-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.0792627933655572 shape=circle style=filled width=0.0792627933655572] + "globular-types.dependent-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-reflexive-globular-types" -> "globular-types.points-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-reflexive-globular-types" -> "globular-types.dependent-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.dependent-reflexive-globular-types" -> "globular-types.globular-types" [arrowhead=none 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width=0.05] + "globular-types.discrete-dependent-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-dependent-reflexive-globular-types" -> "globular-types.discrete-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-dependent-reflexive-globular-types" -> "globular-types.dependent-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-dependent-reflexive-globular-types" -> "globular-types.points-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.discrete-globular-types" -> "globular-types.empty-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-globular-types" -> "foundation.discrete-binary-relations" [arrowhead=none color="#4A755510"] + "globular-types.discrete-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-reflexive-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.068321212351589 shape=circle style=filled width=0.068321212351589] + "globular-types.discrete-reflexive-globular-types" -> "globular-types.symmetric-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-reflexive-globular-types" -> "globular-types.transitive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.discrete-reflexive-globular-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#4A755510"] + "globular-types.discrete-reflexive-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.empty-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.05 shape=circle style=filled width=0.05] + "globular-types.empty-globular-types" -> "foundation.empty-types" [arrowhead=none color="#4A755510"] + "globular-types.empty-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.empty-globular-types" -> "globular-types.constant-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.equality-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.06795090495055724 shape=circle style=filled width=0.06795090495055724] + "globular-types.equality-globular-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#4A755510"] + "globular-types.equality-globular-types" -> "foundation-core.coherently-invertible-maps" [arrowhead=none color="#4A755510"] + "globular-types.equality-globular-types" -> "foundation-core.sections" [arrowhead=none color="#4A755510"] + "globular-types.equality-globular-types" -> 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"globular-types.large-reflexive-globular-maps" -> "globular-types.large-reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" [label="" color="#FFFFFF00" fillcolor="#4A7555" height=0.09622828198609261 shape=circle style=filled width=0.09622828198609261] + "globular-types.large-reflexive-globular-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" -> "foundation.binary-relations" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" -> "foundation.large-binary-relations" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" -> "globular-types.large-globular-maps" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" -> "globular-types.globular-types" [arrowhead=none color="#4A755510"] + "globular-types.large-reflexive-globular-types" -> 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"group-theory.congruence-relations-semigroups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.congruence-relations-semigroups" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.conjugation-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.conjugation-concrete-groups" -> "higher-group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.conjugation-concrete-groups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.conjugation-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10524511819215211 shape=circle style=filled width=0.10524511819215211] + "group-theory.conjugation" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "foundation.transposition-identifications-along-sections" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "foundation.equivalence-extensionality" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "foundation.retractions" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "foundation.transposition-identifications-along-retractions" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.conjugation" -> "foundation.sections" [arrowhead=none color="#96387210"] + "group-theory.contravariant-pushforward-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.contravariant-pushforward-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.contravariant-pushforward-concrete-group-actions" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.0792627933655572 shape=circle style=filled width=0.0792627933655572] + "group-theory.cores-monoids" -> "group-theory.precategory-of-monoids" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "category-theory.functors-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.submonoids" [arrowhead=none color="#96387210"] + "group-theory.cores-monoids" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] + "group-theory.cyclic-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06373568211054055 shape=circle style=filled width=0.06373568211054055] + "group-theory.cyclic-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.cyclic-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.cyclic-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.cyclic-groups" -> "foundation.inhabited-subtypes" [arrowhead=none color="#96387210"] + "group-theory.cyclic-groups" -> "group-theory.generating-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10560411338421884 shape=circle style=filled width=0.10560411338421884] + "group-theory.decidable-subgroups" -> "foundation.decidable-subtypes" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.decidable-subgroups" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.dependent-products-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-abelian-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-abelian-groups" -> "group-theory.dependent-products-groups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.dependent-products-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-commutative-monoids" -> "group-theory.dependent-products-monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] + "group-theory.dependent-products-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-groups" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.dependent-products-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-monoids" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.dependent-products-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.dependent-products-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-group-construction" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] + "group-theory.dihedral-group-construction" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-group-construction" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-group-construction" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-group-construction" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.dihedral-group-construction" -> "foundation.equality-coproduct-types" [arrowhead=none color="#96387210"] + "group-theory.dihedral-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.dihedral-groups" -> "elementary-number-theory.standard-cyclic-groups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.dihedral-groups" -> "group-theory.dihedral-group-construction" [arrowhead=none color="#96387210"] + "group-theory.e8-lattice" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.e8-lattice" -> "foundation.equality-coproduct-types" [arrowhead=none color="#96387210"] + "group-theory.e8-lattice" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.e8-lattice" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.elements-of-finite-order-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "group-theory.orders-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "group-theory.subgroups-generated-by-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "elementary-number-theory.nonzero-integers" [arrowhead=none color="#96387210"] + "group-theory.elements-of-finite-order-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] + "group-theory.embeddings-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.embeddings-abelian-groups" -> "group-theory.embeddings-groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-abelian-groups" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-abelian-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.embeddings-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.embeddings-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.embeddings-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.integer-multiples-of-elements-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.addition-homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#96387210"] + "group-theory.endomorphism-rings-abelian-groups" -> "ring-theory.rings" [arrowhead=none color="#96387210"] + "group-theory.epimorphisms-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.052682459581144495 shape=circle style=filled width=0.052682459581144495] + "group-theory.epimorphisms-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.epimorphisms-groups" -> "category-theory.epimorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.epimorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.epimorphisms-groups" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] + "group-theory.epimorphisms-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] + "group-theory.equivalences-concrete-group-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-group-actions" -> "group-theory.homomorphisms-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-group-actions" -> "foundation.1-types" [arrowhead=none color="#96387210"] + 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[arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-groups" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#96387210"] + "group-theory.equivalences-concrete-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.equivalences-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10208095535698015 shape=circle style=filled width=0.10208095535698015] + "group-theory.equivalences-group-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.equivalences-group-actions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] + 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shape=circle style=filled width=0.055934600764264826] + "group-theory.free-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.free-concrete-group-actions" -> "higher-group-theory.free-higher-group-actions" [arrowhead=none color="#96387210"] + "group-theory.free-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.free-groups-with-one-generator" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] + "group-theory.free-groups-with-one-generator" -> "structured-types.initial-pointed-type-equipped-with-automorphism" [arrowhead=none color="#96387210"] + "group-theory.free-groups-with-one-generator" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.free-groups-with-one-generator" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + 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[arrowhead=none color="#96387210"] + "group-theory.function-abelian-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.function-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.function-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.function-commutative-monoids" -> "group-theory.dependent-products-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.function-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.function-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.function-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.function-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.function-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.function-groups" -> "group-theory.dependent-products-groups" [arrowhead=none color="#96387210"] + "group-theory.function-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.function-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.function-monoids" -> "group-theory.dependent-products-monoids" [arrowhead=none color="#96387210"] + "group-theory.function-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.function-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.function-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.function-semigroups" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] + 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[arrowhead=none color="#96387210"] + "group-theory.functoriality-quotient-groups" -> "group-theory.homomorphisms-groups-equipped-with-normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.functoriality-quotient-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] + "group-theory.furstenberg-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.generating-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13137046916338763 shape=circle style=filled width=0.13137046916338763] + "group-theory.generating-elements-groups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.generating-elements-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] + "group-theory.generating-elements-groups" -> "ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + 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shape=circle style=filled width=0.09424124867625935] + "group-theory.homomorphisms-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-groups" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-groups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] + "group-theory.homomorphisms-monoids" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07814071540843244 shape=circle style=filled width=0.07814071540843244] + "group-theory.homomorphisms-semigroups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-semigroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-semigroups" -> "foundation.homotopy-induction" [arrowhead=none color="#96387210"] + "group-theory.homomorphisms-semigroups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.homotopy-automorphism-groups" -> "foundation.truncation-levels" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.1-types" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "higher-group-theory.automorphism-groups" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.connected-components" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "group-theory.equivalences-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.mere-equality" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.truncations" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.homotopy-automorphism-groups" -> "group-theory.automorphism-groups" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.09069398819863565 shape=circle style=filled width=0.09069398819863565] + "group-theory.images-of-group-homomorphisms" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "foundation.universal-property-image" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "group-theory.pullbacks-subgroups" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "foundation.images" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "foundation.images-subtypes" [arrowhead=none color="#96387210"] + "group-theory.images-of-group-homomorphisms" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.images-of-semigroup-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] + "group-theory.images-of-semigroup-homomorphisms" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] 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color="#96387210"] + "group-theory.images-of-semigroup-homomorphisms" -> "foundation.images-subtypes" [arrowhead=none color="#96387210"] + "group-theory.images-of-semigroup-homomorphisms" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.images-of-semigroup-homomorphisms" -> "group-theory.pullbacks-subsemigroups" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.09329948523165156 shape=circle style=filled width=0.09329948523165156] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "group-theory.multiples-of-elements-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-multiples-of-elements-abelian-groups" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.1258779095300422 shape=circle style=filled width=0.1258779095300422] + "group-theory.integer-powers-of-elements-groups" -> "structured-types.initial-pointed-type-equipped-with-automorphism" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "group-theory.powers-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "group-theory.commuting-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.integer-powers-of-elements-groups" -> "foundation.iterating-automorphisms" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.intersections-subgroups-abelian-groups" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-abelian-groups" -> "group-theory.intersections-subgroups-groups" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "group-theory.intersections-subgroups-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-groups" -> "foundation.intersections-subtypes" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-groups" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#96387210"] + "group-theory.intersections-subgroups-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.inverse-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] + "group-theory.inverse-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.inverse-semigroups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.invertible-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.11683375435392794 shape=circle style=filled width=0.11683375435392794] + "group-theory.invertible-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.invertible-elements-monoids" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.invertible-elements-monoids" -> "foundation.injective-maps" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07667391879499177 shape=circle style=filled width=0.07667391879499177] + "group-theory.isomorphisms-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-abelian-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.isomorphisms-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-concrete-groups" -> "group-theory.precategory-of-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-concrete-groups" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08360063661473255 shape=circle style=filled width=0.08360063661473255] + "group-theory.isomorphisms-group-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "group-theory.precategory-of-group-actions" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-group-actions" -> 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"category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "group-theory.equivalences-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "group-theory.isomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "group-theory.category-of-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.09221140737526 shape=circle style=filled width=0.09221140737526] + "group-theory.isomorphisms-monoids" -> "group-theory.precategory-of-monoids" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-monoids" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-monoids" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08971499589146108 shape=circle style=filled width=0.08971499589146108] + "group-theory.isomorphisms-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "group-theory.equivalences-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "group-theory.precategory-of-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.isomorphisms-semigroups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.0850962943396763 shape=circle style=filled width=0.0850962943396763] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.iterated-cartesian-product-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.truncation-levels" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "group-theory.trivial-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.1-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.truncated-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.mere-equality" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] + "group-theory.iterated-cartesian-products-concrete-groups" -> "group-theory.cartesian-products-concrete-groups" [arrowhead=none color="#96387210"] + 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"group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.truncation-levels" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.1-types" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.fibers-of-maps" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.connected-components" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "foundation.truncated-maps" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.058362862484713576 shape=circle style=filled width=0.058362862484713576] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.embeddings-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.kernels-homomorphisms-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.large-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.large-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.09543843320812216 shape=circle style=filled width=0.09543843320812216] + "group-theory.loop-groups-sets" -> "foundation.truncation-levels" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "foundation.identity-truncated-types" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "foundation.truncated-types" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.loop-groups-sets" -> 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"group-theory.minkowski-multiplication-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "foundation.powersets" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "group-theory.minkowski-multiplication-monoids" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-commutative-monoids" -> "group-theory.subsets-commutative-monoids" [arrowhead=none color="#96387210"] + 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"group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-monoids" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-monoids" -> "foundation.unital-binary-operations" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-monoids" -> "foundation.inhabited-subtypes" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07846294652976578 shape=circle style=filled width=0.07846294652976578] + "group-theory.minkowski-multiplication-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-semigroups" -> "group-theory.subsets-semigroups" [arrowhead=none color="#96387210"] + "group-theory.minkowski-multiplication-semigroups" -> "foundation.conjunction" [arrowhead=none color="#96387210"] + 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color="#96387210"] + "group-theory.monomorphisms-concrete-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.monomorphisms-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.monomorphisms-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.monomorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.monomorphisms-groups" -> "category-theory.monomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.monomorphisms-groups" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] + "group-theory.monomorphisms-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.multiples-of-elements-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] + "group-theory.multiples-of-elements-abelian-groups" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.multiples-of-elements-abelian-groups" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.multiples-of-elements-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.multiples-of-elements-abelian-groups" -> "group-theory.powers-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] + "group-theory.nontrivial-groups" -> "group-theory.trivial-groups" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.propositional-extensionality" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.injective-maps" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.disjunction" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.negation" [arrowhead=none color="#96387210"] + "group-theory.nontrivial-groups" -> "foundation.negated-equality" [arrowhead=none color="#96387210"] + 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-> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.normal-closures-subgroups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.normal-closures-subgroups" -> "group-theory.subgroups-generated-by-subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.normal-closures-subgroups" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#96387210"] + "group-theory.normal-closures-subgroups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.normal-closures-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.normal-cores-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] + "group-theory.normal-cores-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.normal-cores-subgroups" -> 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style=filled width=0.13374970032900724] + "group-theory.normal-subgroups" -> "group-theory.congruence-relations-groups" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] + "group-theory.normal-subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + 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"group-theory.normal-submonoids-commutative-monoids" -> "group-theory.submonoids-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "group-theory.congruence-relations-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.normal-submonoids-commutative-monoids" -> 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"foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06720416904044836 shape=circle style=filled width=0.06720416904044836] + "group-theory.nullifying-group-homomorphisms" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "group-theory.homomorphisms-groups-equipped-with-normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.nullifying-group-homomorphisms" -> "group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.opposite-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.opposite-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.opposite-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.opposite-groups" -> "group-theory.opposite-semigroups" [arrowhead=none color="#96387210"] + "group-theory.opposite-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.opposite-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.opposite-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.orbit-stabilizer-theorem-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.mere-equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] + "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.stabilizer-groups-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.orbits-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.orbits-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.orbits-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.orbits-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.orbits-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.orbits-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.orders-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "group-theory.free-groups-with-one-generator" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.orders-of-elements-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] + "group-theory.perfect-cores" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.perfect-cores" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.perfect-cores" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.perfect-cores" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.perfect-cores" -> "group-theory.perfect-subgroups" [arrowhead=none color="#96387210"] + "group-theory.perfect-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.perfect-groups" -> "group-theory.full-subgroups" [arrowhead=none color="#96387210"] + "group-theory.perfect-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.perfect-groups" -> "group-theory.commutator-subgroups" [arrowhead=none color="#96387210"] + "group-theory.perfect-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.perfect-subgroups" -> "group-theory.perfect-groups" [arrowhead=none color="#96387210"] + "group-theory.perfect-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.perfect-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06887294038719267 shape=circle style=filled width=0.06887294038719267] + "group-theory.powers-of-elements-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-commutative-monoids" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-commutative-monoids" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-commutative-monoids" -> "group-theory.powers-of-elements-monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-commutative-monoids" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06960177486788897 shape=circle style=filled width=0.06960177486788897] + "group-theory.powers-of-elements-groups" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" -> "group-theory.commuting-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-groups" -> "group-theory.powers-of-elements-monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.0911103361631442 shape=circle style=filled width=0.0911103361631442] + "group-theory.powers-of-elements-monoids" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-monoids" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.powers-of-elements-monoids" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-commutative-monoids" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-commutative-monoids" -> "group-theory.precategory-of-monoids" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-commutative-monoids" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-commutative-monoids" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-concrete-groups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-group-actions" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-group-actions" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-group-actions" -> "group-theory.homomorphisms-group-actions" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-groups" -> "group-theory.precategory-of-semigroups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-groups" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-groups" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-groups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-monoids" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" -> "group-theory.precategory-of-semigroups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-monoids" -> "category-theory.large-subprecategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06923831664020327 shape=circle style=filled width=0.06923831664020327] + "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-orbits-monoid-actions" -> "group-theory.monoid-actions" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.precategory-of-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-semigroups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] + "group-theory.precategory-of-semigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.principal-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.principal-group-actions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#96387210"] + "group-theory.principal-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.principal-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] + "group-theory.principal-torsors-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.principal-torsors-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.principal-torsors-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.products-of-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.products-of-elements-monoids" -> "lists.concatenation-lists" [arrowhead=none color="#96387210"] + "group-theory.products-of-elements-monoids" -> "lists.lists" [arrowhead=none color="#96387210"] + "group-theory.products-of-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07683827893814787 shape=circle style=filled width=0.07683827893814787] + "group-theory.pullbacks-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.pullbacks-subsemigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subgroups" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06353743689589825 shape=circle style=filled width=0.06353743689589825] + "group-theory.pullbacks-subsemigroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "group-theory.subsets-semigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#96387210"] + "group-theory.pullbacks-subsemigroups" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06887294038719267 shape=circle style=filled width=0.06887294038719267] + "group-theory.quotient-groups-concrete-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "foundation.0-images-of-maps" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "foundation.1-types" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "group-theory.mere-equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "group-theory.transitive-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "group-theory.normal-subgroups-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "group-theory.equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "foundation.mere-equality" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13440833808089672 shape=circle style=filled width=0.13440833808089672] + "group-theory.quotient-groups" -> "foundation.commuting-triangles-of-maps" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.nullifying-group-homomorphisms" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.contractible-maps" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.surjective-maps" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.binary-functoriality-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotient-groups" -> "group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.089855504976604 shape=circle style=filled width=0.089855504976604] + "group-theory.quotients-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.nullifying-group-homomorphisms" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.surjective-maps" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.binary-functoriality-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.quotients-abelian-groups" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#96387210"] + "group-theory.rational-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] + "group-theory.rational-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.rational-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.rational-commutative-monoids" -> "group-theory.powers-of-elements-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.representations-monoids-precategories" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.059007775570652274 shape=circle style=filled width=0.059007775570652274] + "group-theory.representations-monoids-precategories" -> "category-theory.precategories" [arrowhead=none color="#96387210"] + 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color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "group-theory.congruence-relations-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07484213832213174 shape=circle style=filled width=0.07484213832213174] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] + "group-theory.saturated-congruence-relations-monoids" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] + "group-theory.semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] + "group-theory.semigroups" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#96387210"] + "group-theory.sheargroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.shriek-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.shriek-concrete-group-actions" -> "foundation.set-truncations" [arrowhead=none color="#96387210"] + "group-theory.shriek-concrete-group-actions" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.shriek-concrete-group-actions" -> 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[arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "order-theory.large-preorders" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "order-theory.posets" [arrowhead=none color="#96387210"] + "group-theory.subgroups-abelian-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] + 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-> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#96387210"] + "group-theory.subgroups-concrete-groups" -> "group-theory.orbits-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.subgroups-concrete-groups" -> "group-theory.equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.subgroups-concrete-groups" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] + "group-theory.subgroups-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10071234925192582 shape=circle style=filled width=0.10071234925192582] + "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + 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"foundation.images-subtypes" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.images-of-group-homomorphisms" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.free-groups-with-one-generator" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" -> "foundation.singleton-subtypes" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-elements-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] + "group-theory.subgroups-generated-by-families-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] + "group-theory.subgroups-generated-by-families-of-elements-groups" -> 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color="#FFFFFF00" fillcolor="#963872" height=0.13627262043998845 shape=circle style=filled width=0.13627262043998845] + "group-theory.subgroups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "order-theory.posets" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.injective-maps" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.disjunction" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.large-binary-relations" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "order-theory.large-preorders" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] + "group-theory.subgroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] 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[arrowhead=none color="#96387210"] + "group-theory.subsemigroups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] + "group-theory.subsemigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.subsemigroups" -> "foundation.large-binary-relations" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.subsets-abelian-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] + "group-theory.subsets-abelian-groups" -> "foundation.powersets" [arrowhead=none color="#96387210"] + "group-theory.subsets-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05147120664547112 shape=circle style=filled width=0.05147120664547112] + "group-theory.subsets-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.subsets-commutative-monoids" -> "group-theory.subsets-monoids" [arrowhead=none color="#96387210"] + "group-theory.subsets-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.subsets-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] + "group-theory.subsets-groups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] + "group-theory.subsets-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] + "group-theory.subsets-groups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] + "group-theory.subsets-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] + "group-theory.subsets-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + "group-theory.subsets-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.053631769453388635 shape=circle style=filled width=0.053631769453388635] + "group-theory.subsets-semigroups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] + "group-theory.subsets-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] + "group-theory.subsets-semigroups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] + "group-theory.subsets-semigroups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] + "group-theory.subsets-semigroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] + 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"group-theory.substitution-functor-group-actions" -> "category-theory.functors-large-precategories" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "foundation.equivalence-classes" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "group-theory.homomorphisms-group-actions" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "group-theory.symmetric-groups" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] + "group-theory.substitution-functor-group-actions" -> "foundation.equivalence-relations" [arrowhead=none 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color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "univalent-combinatorics.double-counting" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "group-theory.sums-of-finite-sequences-of-elements-commutative-monoids" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "foundation.inhabited-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-families-of-elements-commutative-monoids" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#96387210"] + 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"elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "finite-group-theory.transpositions-standard-finite-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "group-theory.sums-of-finite-sequences-of-elements-semigroups" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "foundation.negated-equality" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "linear-algebra.finite-sequences-in-commutative-semigroups" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "lists.lists" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-commutative-semigroups" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07261775912465183 shape=circle style=filled width=0.07261775912465183] + "group-theory.sums-of-finite-sequences-of-elements-monoids" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-monoids" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] + "group-theory.sums-of-finite-sequences-of-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] + 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color="#96387210"] + "group-theory.surjective-semigroup-homomorphisms" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] + "group-theory.symmetric-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05147120664547112 shape=circle style=filled width=0.05147120664547112] + "group-theory.symmetric-concrete-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] + "group-theory.symmetric-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] + "group-theory.symmetric-concrete-groups" -> "foundation.mere-equality" [arrowhead=none color="#96387210"] + "group-theory.symmetric-concrete-groups" -> "group-theory.automorphism-groups" [arrowhead=none color="#96387210"] + "group-theory.symmetric-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07501051229944192 shape=circle style=filled width=0.07501051229944192] + "group-theory.symmetric-groups" -> 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color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "foundation.contractible-types" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "group-theory.equivalences-concrete-groups" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.automorphism-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#E79FEE10"] + 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height=0.05 shape=circle style=filled width=0.05] + "higher-group-theory.higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.06131444962281207 shape=circle style=filled width=0.06131444962281207] + "higher-group-theory.higher-groups" -> "foundation.images" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" -> "structured-types.h-spaces" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" -> "foundation.full-subtypes" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" -> "foundation.mere-equality" [arrowhead=none color="#E79FEE10"] + "higher-group-theory.higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] + 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"metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" 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[arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cartesian-products-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] + 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"metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.12855540770864293 shape=circle style=filled width=0.12855540770864293] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.limits-of-sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.archimedean-property-positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.nonzero-natural-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.unit-fractions-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.convergent-sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.multiplicative-group-of-positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.closed-subsets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.located-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08435178051687288 shape=circle style=filled width=0.08435178051687288] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.closure-subsets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.intersections-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.discrete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.dependent-products-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.open-subsets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.dense-subsets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.disjunction" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.dependent-products-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closed-subsets-metric-spaces" -> "foundation.complements-subtypes" 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"metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.closure-subsets-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] + "metric-spaces.closure-subsets-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.closure-subsets-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.compact-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.compact-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.compact-metric-spaces" -> 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"metric-spaces.convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.convergent-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] + "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.limits-of-sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.convergent-sequences-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.closure-subsets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08223128882139645 shape=circle style=filled width=0.08223128882139645] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09557052798858454 shape=circle style=filled width=0.09557052798858454] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.propositional-extensionality" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.locally-constant-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] + "metric-spaces.discrete-metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08146059432173196 shape=circle style=filled width=0.08146059432173196] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "order-theory.preorders" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.inequality-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.negation" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.rational-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.minimum-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] + "metric-spaces.equality-of-metric-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.equality-of-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.retractions" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "foundation.sections" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08021208221262416 shape=circle style=filled width=0.08021208221262416] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.functions-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.isometries-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] + "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.extensionality-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.0686895234426777 shape=circle style=filled width=0.0686895234426777] + "metric-spaces.extensionality-pseudometric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.extensionality-pseudometric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.extensionality-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.extensionality-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.extensionality-pseudometric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] + "metric-spaces.functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functions-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.functions-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.category-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.faithful-functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.category-of-sets" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.maps-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.conservative-functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.isomorphisms-of-sets" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.faithful-functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.split-essentially-surjective-functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.maps-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.conservative-functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.functors-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#923E8210"] + "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-short-functions" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.images-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] + "metric-spaces.images-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-short-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-short-functions-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] + "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09221140737526 shape=circle style=filled width=0.09221140737526] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.discrete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.locally-constant-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.interior-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.interior-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09983164971226559 shape=circle style=filled width=0.09983164971226559] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "foundation.fibers-of-maps" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "foundation.embeddings" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "foundation.injective-maps" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.isometries-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09804652094354867 shape=circle style=filled width=0.09804652094354867] + "metric-spaces.isometries-pseudometric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "metric-spaces.functions-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.isometries-pseudometric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] + "metric-spaces.limits-of-cauchy-approximations-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] + "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-cauchy-approximations-pseudometric-spaces" -> "metric-spaces.cauchy-approximations-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.limits-of-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-functions-metric-spaces" -> "foundation.inhabited-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08450120805741372 shape=circle style=filled width=0.08450120805741372] + "metric-spaces.limits-of-sequences-metric-spaces" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "foundation.inhabited-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.limits-of-sequences-metric-spaces" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.1026970198232252 shape=circle style=filled width=0.1026970198232252] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.elements-at-bounded-distance-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "elementary-number-theory.multiplicative-group-of-positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.inhabited-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] + "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.locally-constant-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "metric-spaces.elements-at-bounded-distance-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.locally-constant-functions-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.067391628732453 shape=circle style=filled width=0.067391628732453] + "metric-spaces.located-metric-spaces" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "metric-spaces.elements-at-bounded-distance-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "real-numbers.real-numbers-from-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "real-numbers.inequality-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.disjunction" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.negation" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "foundation.functoriality-disjunction" [arrowhead=none color="#923E8210"] + "metric-spaces.located-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09557052798858454 shape=circle style=filled width=0.09557052798858454] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.dependent-products-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08192388105819126 shape=circle style=filled width=0.08192388105819126] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "foundation.involutions" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.dependent-products-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.06887294038719267 shape=circle style=filled width=0.06887294038719267] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-space-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.convergent-sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.054564565808626536 shape=circle style=filled width=0.054564565808626536] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.dependent-products-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-isometries-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.metric-space-of-isometries-metric-spaces" -> "metric-spaces.metric-space-of-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-isometries-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-isometries-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-isometries-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-lipschitz-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.metric-space-of-lipschitz-functions-metric-spaces" -> "metric-spaces.lipschitz-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-lipschitz-functions-metric-spaces" -> "metric-spaces.metric-space-of-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-lipschitz-functions-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-lipschitz-functions-metric-spaces" -> "metric-spaces.metric-spaces" 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"elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.lipschitz-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "foundation.diagonal-maps-cartesian-products-of-types" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.multiplication-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.absolute-value-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.distance-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-rational-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-short-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.metric-space-of-short-functions-metric-spaces" -> "metric-spaces.metric-space-of-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-short-functions-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-short-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-space-of-short-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09343460403558627 shape=circle style=filled width=0.09343460403558627] + "metric-spaces.metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.monotonic-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.monotonic-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.monotonic-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.nets-located-metric-spaces" -> "metric-spaces.approximations-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "univalent-combinatorics.finite-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "metric-spaces.located-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "univalent-combinatorics.finitely-enumerable-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "univalent-combinatorics.finitely-enumerable-types" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.surjective-maps" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "metric-spaces.nets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.nets-located-metric-spaces" -> "foundation.singleton-subtypes" [arrowhead=none 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"metric-spaces.open-subsets-located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.open-subsets-located-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "metric-spaces.located-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "foundation.intersections-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> 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color="#923E8210"] + "metric-spaces.open-subsets-located-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08405212848450323 shape=circle style=filled width=0.08405212848450323] + "metric-spaces.open-subsets-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" -> "foundation.intersections-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.open-subsets-metric-spaces" -> 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"metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.preimages-rational-neighborhood-relations" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.preimages-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.preimages-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.preimages-rational-neighborhood-relations" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.preimages-rational-neighborhood-relations" -> "foundation.injective-maps" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08568724792830806 shape=circle style=filled width=0.08568724792830806] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.propositional-extensionality" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.negation" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] + "metric-spaces.pseudometric-spaces" -> 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color="#923E8210"] + "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.absolute-value-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.distance-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.reflexive-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.reflexive-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.reflexive-rational-neighborhood-relations" -> 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"metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.symmetric-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.symmetric-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.symmetric-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.symmetric-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.0668276721338242 shape=circle style=filled width=0.0668276721338242] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.nets-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] + "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.triangular-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] + "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.triangular-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.triangular-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08284268228643028 shape=circle style=filled width=0.08284268228643028] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "metric-spaces.continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "foundation.inhabited-subtypes" [arrowhead=none color="#923E8210"] + "metric-spaces.uniformly-continuous-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] + "modal-type-theory.action-on-homotopies-flat-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05 shape=circle style=filled width=0.05] + "modal-type-theory.action-on-homotopies-flat-modality" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-homotopies-flat-modality" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-homotopies-flat-modality" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-identifications-crisp-functions" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05922118594381655 shape=circle style=filled width=0.05922118594381655] + "modal-type-theory.action-on-identifications-crisp-functions" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-identifications-flat-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05023075432006429 shape=circle style=filled width=0.05023075432006429] + "modal-type-theory.action-on-identifications-flat-modality" -> "modal-type-theory.action-on-identifications-crisp-functions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-identifications-flat-modality" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.action-on-identifications-flat-modality" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.06795090495055724 shape=circle style=filled width=0.06795090495055724] + "modal-type-theory.crisp-cartesian-product-types" -> "foundation.inhabited-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-cartesian-product-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-coproduct-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] + "modal-type-theory.crisp-coproduct-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-coproduct-types" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-coproduct-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-coproduct-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-coproduct-types" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-function-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05964571600864011 shape=circle style=filled width=0.05964571600864011] + "modal-type-theory.crisp-dependent-function-types" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-function-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-function-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-function-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-function-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] + "modal-type-theory.crisp-dependent-pair-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-dependent-pair-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] + "modal-type-theory.crisp-function-types" -> "foundation.postcomposition-functions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "modal-type-theory.crisp-dependent-function-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-function-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-identity-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.067391628732453 shape=circle style=filled width=0.067391628732453] + "modal-type-theory.crisp-identity-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-identity-types" -> "foundation.retracts-of-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-identity-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-identity-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-identity-types" -> "foundation.injective-maps" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-law-of-excluded-middle" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05 shape=circle style=filled width=0.05] + "modal-type-theory.crisp-law-of-excluded-middle" -> "foundation.decidable-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-law-of-excluded-middle" -> "foundation-core.propositions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-law-of-excluded-middle" -> "foundation-core.decidable-propositions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.068321212351589 shape=circle style=filled width=0.068321212351589] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.pullbacks" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.morphisms-cospan-diagrams" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.functoriality-pullbacks" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.crisp-dependent-pair-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-pullbacks" -> "modal-type-theory.action-on-identifications-crisp-functions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.crisp-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05 shape=circle style=filled width=0.05] + "modal-type-theory.dependent-universal-property-flat-discrete-crisp-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05 shape=circle style=filled width=0.05] + "modal-type-theory.dependent-universal-property-flat-discrete-crisp-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.0911103361631442 shape=circle style=filled width=0.0911103361631442] + "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.action-on-homotopies-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "foundation.embeddings" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "foundation.booleans" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "foundation.empty-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-discrete-crisp-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.06510649876675342 shape=circle style=filled width=0.06510649876675342] + "modal-type-theory.flat-modality" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-modality" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.06942028362060094 shape=circle style=filled width=0.06942028362060094] + "modal-type-theory.flat-sharp-adjunction" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "modal-type-theory.sharp-codiscrete-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.flat-sharp-adjunction" -> "modal-type-theory.sharp-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-flat-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.07085919892526085 shape=circle style=filled width=0.07085919892526085] + "modal-type-theory.functoriality-flat-modality" -> "modal-type-theory.action-on-identifications-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-flat-modality" -> "foundation.retractions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-flat-modality" -> "foundation.retracts-of-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-flat-modality" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-flat-modality" -> "foundation.sections" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-sharp-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05 shape=circle style=filled width=0.05] + "modal-type-theory.functoriality-sharp-modality" -> "orthogonal-factorization-systems.modal-induction" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-sharp-modality" -> "orthogonal-factorization-systems.locally-small-modal-operators" [arrowhead=none color="#E45F8510"] + "modal-type-theory.functoriality-sharp-modality" -> 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[arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-codiscrete-types" -> "orthogonal-factorization-systems.higher-modalities" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-codiscrete-types" -> "foundation.embeddings" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-codiscrete-types" -> "foundation.transport-along-equivalences" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-codiscrete-types" -> "modal-type-theory.sharp-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-modality" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.10146115026262832 shape=circle style=filled width=0.10146115026262832] + "modal-type-theory.sharp-modality" -> "orthogonal-factorization-systems.modal-induction" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-modality" -> "orthogonal-factorization-systems.locally-small-modal-operators" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-modality" -> "orthogonal-factorization-systems.modal-subuniverse-induction" [arrowhead=none color="#E45F8510"] + "modal-type-theory.sharp-modality" -> "foundation.locally-small-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.transport-along-crisp-identifications" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.0647177997777583 shape=circle style=filled width=0.0647177997777583] + "modal-type-theory.transport-along-crisp-identifications" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "foundation.postcomposition-functions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "modal-type-theory.crisp-function-types" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "foundation.universal-property-equivalences" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "modal-type-theory.action-on-identifications-crisp-functions" [arrowhead=none color="#E45F8510"] + "modal-type-theory.universal-property-flat-discrete-crisp-types" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] + "order-theory.accessible-elements-relations" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06549289087570129 shape=circle style=filled width=0.06549289087570129] + "order-theory.accessible-elements-relations" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.accessible-elements-relations" -> "foundation-core.propositions" [arrowhead=none color="#533A2210"] + "order-theory.accessible-elements-relations" -> "foundation-core.negation" [arrowhead=none color="#533A2210"] + "order-theory.bottom-elements-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.bottom-elements-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.bottom-elements-large-posets" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.bottom-elements-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.bottom-elements-posets" -> "order-theory.bottom-elements-preorders" [arrowhead=none color="#533A2210"] + "order-theory.bottom-elements-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.bottom-elements-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.bottom-elements-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] + "order-theory.chains-posets" -> "order-theory.chains-preorders" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "foundation.existential-quantification" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "foundation.disjunction" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.chains-posets" -> "foundation.images" [arrowhead=none color="#533A2210"] + "order-theory.chains-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05023075432006429 shape=circle style=filled width=0.05023075432006429] + "order-theory.chains-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.chains-preorders" -> "order-theory.total-preorders" [arrowhead=none color="#533A2210"] + "order-theory.chains-preorders" -> "order-theory.subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.10749850860545447 shape=circle style=filled width=0.10749850860545447] + "order-theory.closure-operators-large-locales" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-frames" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.closure-operators-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-meet-subsemilattices" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-locales" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07226947050238228 shape=circle style=filled width=0.07226947050238228] + "order-theory.closure-operators-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-posets" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-posets" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.closure-operators-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-galois-connections-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] + "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#533A2210"] + "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.coverings-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.coverings-locales" -> "order-theory.locales" [arrowhead=none color="#533A2210"] + "order-theory.decidable-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] + "order-theory.decidable-posets" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-posets" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] + "order-theory.decidable-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.decidable-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] + "order-theory.decidable-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subposets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.decidable-subposets" -> "foundation.decidable-subtypes" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subposets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subposets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subposets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subpreorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.decidable-subpreorders" -> "foundation.decidable-subtypes" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subpreorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subpreorders" -> "order-theory.subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-subpreorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.1234491685859344 shape=circle style=filled width=0.1234491685859344] + "order-theory.decidable-total-orders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.decidable-posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.decidable-total-preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.greatest-lower-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.join-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-orders" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] + "order-theory.decidable-total-preorders" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "order-theory.total-preorders" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] + "order-theory.decidable-total-preorders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] + "order-theory.deflationary-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] + "order-theory.deflationary-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.deflationary-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.deflationary-maps-posets" -> "order-theory.deflationary-maps-preorders" [arrowhead=none color="#533A2210"] + "order-theory.deflationary-maps-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] + "order-theory.deflationary-maps-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] + "order-theory.deflationary-maps-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06942028362060094 shape=circle style=filled width=0.06942028362060094] + "order-theory.dependent-products-large-frames" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.dependent-products-large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.dependent-products-large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.large-frames" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-frames" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-inflattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.059007775570652274 shape=circle style=filled width=0.059007775570652274] + "order-theory.dependent-products-large-inflattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-inflattices" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-inflattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-inflattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-inflattices" -> "order-theory.large-inflattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0629389547650211 shape=circle style=filled width=0.0629389547650211] + "order-theory.dependent-products-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-locales" -> "order-theory.dependent-products-large-frames" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06606824211104302 shape=circle style=filled width=0.06606824211104302] + "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.dependent-products-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-posets" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-posets" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-posets" -> "order-theory.dependent-products-large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.dependent-products-large-preorders" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-preorders" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] + "order-theory.dependent-products-large-suplattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-suplattices" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-suplattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-suplattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.dependent-products-large-suplattices" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.distributive-lattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] + "order-theory.distributive-lattices" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.distributive-lattices" -> "order-theory.lattices" [arrowhead=none color="#533A2210"] + "order-theory.distributive-lattices" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.distributive-lattices" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.distributive-lattices" -> "order-theory.join-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.finite-coverings-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.finite-coverings-locales" -> "order-theory.locales" [arrowhead=none color="#533A2210"] + "order-theory.finite-coverings-locales" -> "order-theory.coverings-locales" [arrowhead=none color="#533A2210"] + "order-theory.finite-coverings-locales" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.finite-posets" -> "order-theory.finite-preorders" [arrowhead=none color="#533A2210"] + "order-theory.finite-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.finite-posets" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.finite-posets" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07797910051895961 shape=circle style=filled width=0.07797910051895961] + "order-theory.finite-preorders" -> "order-theory.decidable-subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "foundation.decidable-equality" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "foundation.mere-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#533A2210"] + "order-theory.finite-preorders" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.finite-total-orders" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] + "order-theory.finite-total-orders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] + "order-theory.finite-total-orders" -> "order-theory.finite-posets" [arrowhead=none color="#533A2210"] + "order-theory.finite-total-orders" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.finite-total-orders" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.14145108846852988 shape=circle style=filled width=0.14145108846852988] + "order-theory.finitely-graded-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.embeddings" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "elementary-number-theory.modular-arithmetic" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.injective-maps" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "elementary-number-theory.inequality-standard-finite-types" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "order-theory.bottom-elements-posets" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "order-theory.top-elements-posets" [arrowhead=none color="#533A2210"] + "order-theory.finitely-graded-posets" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] + "order-theory.frames" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.08314669315133152 shape=circle style=filled width=0.08314669315133152] + "order-theory.frames" -> "order-theory.greatest-lower-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "order-theory.meet-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "order-theory.suplattices" [arrowhead=none color="#533A2210"] + "order-theory.frames" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.12677669221435825 shape=circle style=filled width=0.12677669221435825] + "order-theory.galois-connections-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.principal-lower-sets-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections-large-posets" -> "order-theory.principal-upper-sets-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.1175871811210872 shape=circle style=filled width=0.1175871811210872] + "order-theory.galois-connections" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections" -> "foundation.subtype-identity-principle" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.galois-connections" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07484213832213174 shape=circle style=filled width=0.07484213832213174] + "order-theory.greatest-lower-bounds-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-large-posets" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-large-posets" -> "order-theory.lower-bounds-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.09397313647244782 shape=circle style=filled width=0.09397313647244782] + "order-theory.greatest-lower-bounds-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-posets" -> "order-theory.lower-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.greatest-lower-bounds-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-frames" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-frames" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-frames" -> "order-theory.homomorphisms-meet-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-frames" -> "order-theory.frames" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-frames" -> "order-theory.homomorphisms-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-frames" -> "order-theory.homomorphisms-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-frames" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-large-frames" -> "order-theory.large-frames" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-frames" -> "order-theory.homomorphisms-large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-frames" -> "order-theory.homomorphisms-large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-large-locales" -> "order-theory.homomorphisms-large-frames" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05073057513131416 shape=circle style=filled width=0.05073057513131416] + "order-theory.homomorphisms-large-meet-semilattices" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-meet-semilattices" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-large-suplattices" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-large-suplattices" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06192863306205975 shape=circle style=filled width=0.06192863306205975] + "order-theory.homomorphisms-meet-semilattices" -> "order-theory.greatest-lower-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-semilattices" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-semilattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-semilattices" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-meet-suplattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-suplattices" -> "order-theory.meet-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-suplattices" -> "order-theory.homomorphisms-meet-semilattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-meet-suplattices" -> "order-theory.homomorphisms-suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.homomorphisms-suplattices" -> "order-theory.suplattices" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-suplattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.homomorphisms-suplattices" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.ideals-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.ideals-preorders" -> "order-theory.lower-types-preorders" [arrowhead=none color="#533A2210"] + "order-theory.ideals-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.ideals-preorders" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.incidence-algebras" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" -> "order-theory.locally-finite-posets" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" -> "order-theory.interval-subposets" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] + "order-theory.incidence-algebras" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] + "order-theory.increasing-sequences-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "lists.sequences" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.increasing-sequences-posets" -> "order-theory.sequences-posets" [arrowhead=none color="#533A2210"] + "order-theory.inflationary-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] + "order-theory.inflationary-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.inflationary-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.inflationary-maps-posets" -> "order-theory.inflationary-maps-preorders" [arrowhead=none color="#533A2210"] + "order-theory.inflationary-maps-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] + "order-theory.inflationary-maps-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] + "order-theory.inflationary-maps-preorders" -> 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"order-theory.inhabited-chains-posets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "order-theory.chains-posets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "order-theory.total-preorders" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "foundation.conjunction" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "foundation.existential-quantification" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "foundation.inhabited-subtypes" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-chains-posets" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] + 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"order-theory.inhabited-finite-total-orders" -> "order-theory.finite-total-orders" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-finite-total-orders" -> "order-theory.finite-posets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-finite-total-orders" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-finite-total-orders" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] + "order-theory.inhabited-finite-total-orders" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] + "order-theory.interval-subposets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.interval-subposets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.interval-subposets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] + "order-theory.interval-subposets" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] + "order-theory.interval-subposets" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.08829760823402076 shape=circle style=filled width=0.08829760823402076] + "order-theory.join-preserving-maps-posets" -> "foundation.small-types" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" -> "foundation.subtype-identity-principle" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" -> "foundation.raising-universe-levels" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" -> "foundation.booleans" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.join-preserving-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + 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"category-theory.precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-posets" -> "order-theory.precategory-of-posets" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.precategory-of-finite-total-orders" -> "order-theory.finite-total-orders" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-total-orders" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-total-orders" -> "category-theory.large-precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-total-orders" -> "category-theory.precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-finite-total-orders" -> "order-theory.precategory-of-posets" [arrowhead=none color="#533A2210"] + 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"order-theory.precategory-of-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-posets" -> "category-theory.large-precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-posets" -> "category-theory.precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.precategory-of-total-orders" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-total-orders" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-total-orders" -> "category-theory.large-precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-total-orders" -> "category-theory.precategories" [arrowhead=none color="#533A2210"] + "order-theory.precategory-of-total-orders" -> "order-theory.precategory-of-posets" [arrowhead=none color="#533A2210"] + "order-theory.preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] + "order-theory.preorders" -> "category-theory.precategories" [arrowhead=none color="#533A2210"] + "order-theory.preorders" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.preorders" -> "foundation.negated-equality" [arrowhead=none color="#533A2210"] + "order-theory.preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.principal-lower-sets-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] + "order-theory.principal-lower-sets-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.principal-lower-sets-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.principal-lower-sets-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.principal-lower-sets-large-posets" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.principal-lower-sets-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] + "order-theory.principal-upper-sets-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] + "order-theory.principal-upper-sets-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.principal-upper-sets-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.principal-upper-sets-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.principal-upper-sets-large-posets" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] + "order-theory.principal-upper-sets-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] + "order-theory.reflective-galois-connections-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.reflective-galois-connections-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.reflective-galois-connections-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.reflective-galois-connections-large-posets" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] + "order-theory.resizing-posets" -> "foundation.small-types" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "foundation.injective-maps" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "foundation.negated-equality" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "order-theory.resizing-preorders" [arrowhead=none color="#533A2210"] + "order-theory.resizing-posets" -> "order-theory.precategory-of-posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.resizing-preorders" -> "foundation.small-types" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" -> "foundation.negated-equality" [arrowhead=none color="#533A2210"] + "order-theory.resizing-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.resizing-suplattices" -> "foundation.small-types" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "order-theory.resizing-posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "foundation.injective-maps" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "order-theory.suplattices" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "foundation.negated-equality" [arrowhead=none color="#533A2210"] + "order-theory.resizing-suplattices" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] + "order-theory.sequences-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05073057513131416 shape=circle style=filled width=0.05073057513131416] + "order-theory.sequences-posets" -> "order-theory.sequences-preorders" [arrowhead=none color="#533A2210"] + "order-theory.sequences-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.sequences-posets" -> "lists.sequences" [arrowhead=none color="#533A2210"] + "order-theory.sequences-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.sequences-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.sequences-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.sequences-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.sequences-preorders" -> "lists.sequences" [arrowhead=none color="#533A2210"] + "order-theory.sequences-strictly-preordered-sets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.sequences-strictly-preordered-sets" -> "lists.sequences" [arrowhead=none color="#533A2210"] + "order-theory.sequences-strictly-preordered-sets" -> "order-theory.strictly-preordered-sets" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06529998061608358 shape=circle style=filled width=0.06529998061608358] + "order-theory.similarity-of-elements-large-posets" -> "foundation.torsorial-type-families" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-posets" -> "order-theory.similarity-of-elements-large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-posets" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-posets" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] + "order-theory.similarity-of-elements-large-preorders" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-preorders" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.10021004013899694 shape=circle style=filled width=0.10021004013899694] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.conjunction" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "order-theory.strict-orders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "order-theory.large-strict-preorders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "order-theory.large-strict-orders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "order-theory.similarity-of-elements-large-strict-preorders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.torsorial-type-families" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-orders" -> "foundation.equivalence-relations" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.09907053327553424 shape=circle style=filled width=0.09907053327553424] + "order-theory.similarity-of-elements-large-strict-preorders" -> "foundation.conjunction" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-elements-large-strict-preorders" -> "foundation.logical-equivalences" 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"order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.similarity-of-order-preserving-maps-large-preorders" -> "order-theory.similarity-of-elements-large-preorders" [arrowhead=none color="#533A2210"] + "order-theory.strict-order-preserving-maps" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07700228825802675 shape=circle style=filled width=0.07700228825802675] + "order-theory.strict-order-preserving-maps" -> "order-theory.strict-preorders" [arrowhead=none color="#533A2210"] + "order-theory.strict-order-preserving-maps" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.strict-order-preserving-maps" -> "order-theory.strictly-preordered-sets" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.068321212351589 shape=circle style=filled width=0.068321212351589] + "order-theory.strict-orders" -> "order-theory.strict-preorders" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "order-theory.strictly-preordered-sets" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "order-theory.similarity-of-elements-strict-preorders" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] + "order-theory.strict-orders" -> "foundation.equivalence-relations" [arrowhead=none color="#533A2210"] + "order-theory.strict-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.strict-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.strict-preorders" -> "foundation.negation" [arrowhead=none color="#533A2210"] + "order-theory.strict-preorders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] + "order-theory.strictly-increasing-sequences-strictly-preordered-sets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] + "order-theory.strictly-increasing-sequences-strictly-preordered-sets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#533A2210"] + "order-theory.strictly-increasing-sequences-strictly-preordered-sets" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#533A2210"] + "order-theory.strictly-increasing-sequences-strictly-preordered-sets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#533A2210"] + "order-theory.strictly-increasing-sequences-strictly-preordered-sets" -> "lists.sequences" [arrowhead=none color="#533A2210"] + 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shape=circle style=filled width=0.05] + "order-theory.top-elements-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] + "order-theory.top-elements-large-posets" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] + "order-theory.top-elements-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.top-elements-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] + "order-theory.top-elements-posets" -> "order-theory.top-elements-preorders" [arrowhead=none color="#533A2210"] + "order-theory.top-elements-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] + "order-theory.top-elements-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.11520267728876608 shape=circle style=filled 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color="#533A2210"] + "order-theory.upper-sets-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] + "order-theory.well-founded-relations" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.060901553009402865 shape=circle style=filled width=0.060901553009402865] + "order-theory.well-founded-relations" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] + "order-theory.well-founded-relations" -> "order-theory.accessible-elements-relations" [arrowhead=none color="#533A2210"] + "order-theory.well-founded-relations" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] + "order-theory.zorns-lemma" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05922118594381655 shape=circle style=filled width=0.05922118594381655] + "order-theory.zorns-lemma" -> "foundation-core.coproduct-types" [arrowhead=none color="#533A2210"] + "order-theory.zorns-lemma" -> "order-theory.upper-bounds-chains-posets" [arrowhead=none color="#533A2210"] 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"real-numbers.rational-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.sections" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.embeddings" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.rational-lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "foundation.retractions" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.raising-universe-levels-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.rational-upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.05 shape=circle style=filled width=0.05] + "real-numbers.rational-upper-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.rational-upper-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.disjoint-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.complements-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.inhabited-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.disjoint-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.complements-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.inhabited-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.06549289087570129 shape=circle style=filled width=0.06549289087570129] + "real-numbers.similarity-real-numbers" -> "order-theory.large-posets" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "foundation.powersets" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.similarity-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.12826066813621598 shape=circle style=filled width=0.12826066813621598] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.inequality-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.additive-group-of-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.arithmetically-located-dedekind-cuts" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.large-binary-relations" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.addition-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "group-theory.abelian-groups" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.binary-transport" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.negation-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "foundation.functoriality-disjunction" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.subsets-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.05 shape=circle style=filled width=0.05] + "real-numbers.subsets-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.subsets-real-numbers" -> "foundation.images-subtypes" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.07749223352929716 shape=circle style=filled width=0.07749223352929716] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "order-theory.upper-bounds-large-posets" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.inequality-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.positive-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.subsets-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.strict-inequality-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] + "real-numbers.suprema-families-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + 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"real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.strict-inequality-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.07156780854205468 shape=circle style=filled width=0.07156780854205468] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.truncation-levels" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.universal-quantification" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.powersets" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "foundation.truncated-types" [arrowhead=none color="#B6687710"] + "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] + "reflection.abstractions" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.abstractions" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.arguments" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] + "reflection.boolean-reflection" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.boolean-reflection" -> "foundation-core.coproduct-types" [arrowhead=none color="#00000010"] + "reflection.boolean-reflection" -> "foundation.booleans" [arrowhead=none color="#00000010"] + "reflection.boolean-reflection" -> "foundation-core.empty-types" [arrowhead=none color="#00000010"] + "reflection.boolean-reflection" -> "foundation.decidable-types" [arrowhead=none color="#00000010"] + "reflection.definitions" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.07683827893814787 shape=circle style=filled width=0.07683827893814787] + "reflection.definitions" -> "reflection.literals" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "reflection.abstractions" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "reflection.terms" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "reflection.names" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "reflection.arguments" [arrowhead=none color="#00000010"] + "reflection.definitions" -> "foundation.empty-types" [arrowhead=none color="#00000010"] + "reflection.erasing-equality" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.fixity" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.fixity" -> "reflection.names" [arrowhead=none color="#00000010"] + "reflection.fixity" -> "primitives.floats" [arrowhead=none color="#00000010"] + "reflection.fixity" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#00000010"] + "reflection.group-solver" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.10959056763571512 shape=circle style=filled width=0.10959056763571512] + "reflection.group-solver" -> "lists.concatenation-lists" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "group-theory.groups" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "foundation.decidable-types" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "lists.functoriality-lists" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "lists.reversing-lists" [arrowhead=none color="#00000010"] + "reflection.group-solver" -> "lists.tuples" [arrowhead=none color="#00000010"] + "reflection.literals" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.literals" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.literals" -> "reflection.metavariables" [arrowhead=none color="#00000010"] + "reflection.literals" -> "primitives.machine-integers" [arrowhead=none color="#00000010"] + "reflection.literals" -> "reflection.names" [arrowhead=none color="#00000010"] + "reflection.literals" -> "primitives.characters" [arrowhead=none color="#00000010"] + "reflection.literals" -> "primitives.floats" [arrowhead=none color="#00000010"] + "reflection.metavariables" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.metavariables" -> "foundation.booleans" [arrowhead=none color="#00000010"] + "reflection.metavariables" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.metavariables" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.names" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.names" -> "foundation.booleans" [arrowhead=none color="#00000010"] + "reflection.names" -> "primitives.machine-integers" [arrowhead=none color="#00000010"] + "reflection.names" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.08700221858486124 shape=circle style=filled width=0.08700221858486124] + "reflection.precategory-solver" -> "lists.concatenation-lists" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" -> "reflection.type-checking-monad" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" -> "category-theory.precategories" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" -> "reflection.terms" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.precategory-solver" -> "reflection.arguments" [arrowhead=none color="#00000010"] + "reflection.rewriting" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] + "reflection.terms" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] + "reflection.terms" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.terms" -> "reflection.abstractions" [arrowhead=none color="#00000010"] + "reflection.terms" -> "reflection.literals" [arrowhead=none color="#00000010"] + "reflection.terms" -> "reflection.metavariables" [arrowhead=none color="#00000010"] + "reflection.terms" -> "reflection.names" [arrowhead=none color="#00000010"] + "reflection.terms" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.terms" -> "reflection.arguments" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.09477519770089146 shape=circle style=filled width=0.09477519770089146] + "reflection.type-checking-monad" -> "primitives.strings" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "reflection.metavariables" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "reflection.definitions" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "reflection.terms" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "foundation.booleans" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "reflection.names" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "lists.lists" [arrowhead=none color="#00000010"] + "reflection.type-checking-monad" -> "reflection.arguments" [arrowhead=none color="#00000010"] + "ring-theory.additive-orders-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06432675209026768 shape=circle style=filled width=0.06432675209026768] + "ring-theory.additive-orders-of-elements-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "group-theory.subgroups" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "group-theory.normal-subgroups" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "group-theory.subsets-groups" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "group-theory.orders-of-elements-groups" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.additive-orders-of-elements-rings" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.algebras-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07226947050238228 shape=circle style=filled width=0.07226947050238228] + "ring-theory.algebras-rings" -> "linear-algebra.left-modules-rings" [arrowhead=none color="#1A127710"] + "ring-theory.algebras-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-sequences-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08269025771888006 shape=circle style=filled width=0.08269025771888006] + "ring-theory.arithmetic-sequences-semirings" -> "foundation.binary-transport" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-sequences-semirings" -> "lists.sequences" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-sequences-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-sequences-semirings" -> "group-theory.arithmetic-sequences-semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-sequences-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08099465764396384 shape=circle style=filled width=0.08099465764396384] + "ring-theory.arithmetic-series-semirings" -> "elementary-number-theory.triangular-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "ring-theory.arithmetic-sequences-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "ring-theory.partial-sums-sequences-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "ring-theory.sums-of-finite-sequences-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "lists.finite-sequences" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "elementary-number-theory.commutative-semiring-of-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.arithmetic-series-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06644904204903672 shape=circle style=filled width=0.06644904204903672] + "ring-theory.binomial-theorem-rings" -> "linear-algebra.finite-sequences-in-rings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "ring-theory.binomial-theorem-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "ring-theory.sums-of-finite-sequences-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "ring-theory.powers-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "elementary-number-theory.binomial-coefficients" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.14180738900393866 shape=circle style=filled width=0.14180738900393866] + "ring-theory.binomial-theorem-semirings" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "linear-algebra.finite-sequences-in-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "ring-theory.sums-of-finite-sequences-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "elementary-number-theory.binomial-coefficients" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.binomial-theorem-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] + "ring-theory.category-of-cyclic-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "category-theory.large-precategories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "category-theory.categories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "ring-theory.homomorphisms-cyclic-rings" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "ring-theory.cyclic-rings" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "ring-theory.category-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-cyclic-rings" -> "category-theory.large-categories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.category-of-rings" -> "category-theory.large-categories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-rings" -> "category-theory.categories" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.category-of-rings" -> "ring-theory.isomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.central-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] + "ring-theory.central-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.central-elements-rings" -> "ring-theory.central-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.central-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] + "ring-theory.central-elements-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.central-elements-semirings" -> "group-theory.central-elements-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.characteristics-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.characteristics-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.characteristics-rings" -> "ring-theory.kernels-of-ring-homomorphisms" [arrowhead=none color="#1A127710"] + "ring-theory.characteristics-rings" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.characteristics-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.commuting-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07191949522280762 shape=circle style=filled width=0.07191949522280762] + "ring-theory.commuting-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.commuting-elements-rings" -> "group-theory.commuting-elements-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.0816153154380072 shape=circle style=filled width=0.0816153154380072] + "ring-theory.congruence-relations-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "group-theory.congruence-relations-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "ring-theory.congruence-relations-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-rings" -> "foundation.equivalence-relations" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07433472814399888 shape=circle style=filled width=0.07433472814399888] + "ring-theory.congruence-relations-semirings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.congruence-relations-semirings" -> "foundation.equivalence-relations" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.11243164449837473 shape=circle style=filled width=0.11243164449837473] + "ring-theory.cyclic-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "group-theory.cyclic-groups" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "foundation.surjective-maps" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "group-theory.free-groups-with-one-generator" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.cyclic-rings" -> "group-theory.generating-elements-groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "ring-theory.ring-extensions-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "ring-theory.dependent-products-rings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "elementary-number-theory.positive-integers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-ring-extensions-rational-numbers" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.067391628732453 shape=circle style=filled width=0.067391628732453] + "ring-theory.dependent-products-rings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "group-theory.dependent-products-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "ring-theory.dependent-products-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] + "ring-theory.dependent-products-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" -> "group-theory.dependent-products-commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" -> "group-theory.dependent-products-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.dependent-products-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.division-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.division-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.division-rings" -> "ring-theory.trivial-rings" [arrowhead=none color="#1A127710"] + "ring-theory.division-rings" -> "foundation.negated-equality" [arrowhead=none color="#1A127710"] + "ring-theory.division-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.free-rings-with-one-generator" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.free-rings-with-one-generator" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.free-rings-with-one-generator" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] + "ring-theory.full-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "foundation.full-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.full-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07534613148009645 shape=circle style=filled width=0.07534613148009645] + "ring-theory.function-rings" -> "foundation.evaluation-functions" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "group-theory.endomorphism-rings-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "ring-theory.dependent-products-rings" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "linear-algebra.left-modules-rings" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "foundation.constant-maps" [arrowhead=none color="#1A127710"] + "ring-theory.function-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.function-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "ring-theory.function-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.function-semirings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.function-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.function-semirings" -> "ring-theory.dependent-products-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.generating-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.generating-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.generating-elements-rings" -> "group-theory.generating-elements-groups" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08299482691834507 shape=circle style=filled width=0.08299482691834507] + "ring-theory.geometric-sequences-semirings" -> "foundation.binary-transport" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" -> "lists.sequences" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" -> "group-theory.arithmetic-sequences-semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.geometric-sequences-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08223128882139645 shape=circle style=filled width=0.08223128882139645] + "ring-theory.groups-of-units-rings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "category-theory.functors-large-precategories" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.cores-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.submonoids" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "group-theory.precategory-of-groups" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.groups-of-units-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07330937243946685 shape=circle style=filled width=0.07330937243946685] + "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.cyclic-rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.homomorphisms-ring-extensions-rational-numbers" -> "ring-theory.ring-extensions-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.10440266230183348 shape=circle style=filled width=0.10440266230183348] + "ring-theory.homomorphisms-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.09570244044334736 shape=circle style=filled width=0.09570244044334736] + "ring-theory.homomorphisms-semirings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12416245902899892 shape=circle style=filled width=0.12416245902899892] + "ring-theory.ideals-generated-by-subsets-rings" -> "lists.concatenation-lists" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "lists.functoriality-lists" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "lists.lists" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12013449149639914 shape=circle style=filled width=0.12013449149639914] + "ring-theory.ideals-rings" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.binary-transport" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "ring-theory.congruence-relations-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "group-theory.congruence-relations-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-rings" -> "foundation.equivalence-relations" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.089855504976604 shape=circle style=filled width=0.089855504976604] + "ring-theory.ideals-semirings" -> "ring-theory.subsets-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.ideals-semirings" -> "group-theory.submonoids" [arrowhead=none color="#1A127710"] + "ring-theory.idempotent-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.idempotent-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.initial-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.initial-rings" -> "category-theory.initial-objects-large-categories" [arrowhead=none color="#1A127710"] + "ring-theory.initial-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.initial-rings" -> "ring-theory.category-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.11343701453127879 shape=circle style=filled width=0.11343701453127879] + "ring-theory.integer-multiples-of-elements-rings" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "ring-theory.commuting-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "ring-theory.multiples-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "group-theory.integer-multiples-of-elements-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.integer-multiples-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] + "ring-theory.intersections-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" -> "foundation.intersections-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.intersections-ideals-semirings" -> "foundation.intersections-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-semirings" -> "ring-theory.ideals-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.intersections-ideals-semirings" -> "ring-theory.subsets-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.invariant-basis-property-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.invariant-basis-property-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#1A127710"] + "ring-theory.invariant-basis-property-rings" -> "ring-theory.isomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.invariant-basis-property-rings" -> "ring-theory.dependent-products-rings" [arrowhead=none color="#1A127710"] + "ring-theory.invariant-basis-property-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.invertible-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.11209451736914716 shape=circle style=filled width=0.11209451736914716] + "ring-theory.invertible-elements-rings" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.invertible-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.invertible-elements-rings" -> "foundation.contractible-types" [arrowhead=none color="#1A127710"] + "ring-theory.invertible-elements-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#1A127710"] + "ring-theory.invertible-elements-rings" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.11822915412357952 shape=circle style=filled width=0.11822915412357952] + "ring-theory.isomorphisms-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "group-theory.isomorphisms-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.contractible-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.homotopy-induction" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.implicit-function-types" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.structure-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "foundation.multivariable-homotopies" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "group-theory.isomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.isomorphisms-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07467338469517418 shape=circle style=filled width=0.07467338469517418] + "ring-theory.joins-ideals-rings" -> "order-theory.large-suplattices" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "ring-theory.ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07584677573504928 shape=circle style=filled width=0.07584677573504928] + "ring-theory.joins-left-ideals-rings" -> "order-theory.large-suplattices" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "ring-theory.left-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "ring-theory.poset-of-left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07584677573504928 shape=circle style=filled width=0.07584677573504928] + "ring-theory.joins-right-ideals-rings" -> "order-theory.large-suplattices" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "ring-theory.right-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "ring-theory.poset-of-right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.joins-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.kernels-of-ring-homomorphisms" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.kernels-of-ring-homomorphisms" -> "group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12086734486480535 shape=circle style=filled width=0.12086734486480535] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "lists.concatenation-lists" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.poset-of-left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "lists.functoriality-lists" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "lists.lists" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] + "ring-theory.left-ideals-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.left-ideals-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.local-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.local-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.local-rings" -> "foundation.disjunction" [arrowhead=none color="#1A127710"] + "ring-theory.local-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08435178051687288 shape=circle style=filled width=0.08435178051687288] + "ring-theory.localizations-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "foundation.contractible-types" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#1A127710"] + "ring-theory.localizations-rings" -> "foundation.contractible-maps" [arrowhead=none color="#1A127710"] + "ring-theory.maximal-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.multiples-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] + "ring-theory.multiples-of-elements-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.multiples-of-elements-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.multiples-of-elements-rings" -> "group-theory.multiples-of-elements-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.multiples-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.multiplicative-orders-of-units-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.nil-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.nil-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nil-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nil-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nil-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.nil-ideals-rings" -> "ring-theory.nilpotent-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.052682459581144495 shape=circle style=filled width=0.052682459581144495] + "ring-theory.nilpotent-elements-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-rings" -> "ring-theory.nilpotent-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-rings" -> "ring-theory.powers-of-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-rings" -> "foundation.existential-quantification" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.055708601453115555 shape=circle style=filled width=0.055708601453115555] + "ring-theory.nilpotent-elements-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-semirings" -> "ring-theory.binomial-theorem-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-semirings" -> "foundation.existential-quantification" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.nilpotent-elements-semirings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.ring-extensions-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-ring-extensions-rational-numbers" -> "elementary-number-theory.positive-integers" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.opposite-rings" [arrowhead=none color="#1A127710"] + "ring-theory.opposite-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.opposite-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.partial-sums-sequences-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.partial-sums-sequences-semirings" -> "ring-theory.sums-of-finite-sequences-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.partial-sums-sequences-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.partial-sums-sequences-semirings" -> "lists.sequences" [arrowhead=none color="#1A127710"] + "ring-theory.partial-sums-sequences-semirings" -> "lists.finite-sequences" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.poset-of-cyclic-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-cyclic-rings" -> "ring-theory.category-of-cyclic-rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06373568211054055 shape=circle style=filled width=0.06373568211054055] + "ring-theory.poset-of-ideals-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "order-theory.large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] + "ring-theory.poset-of-left-ideals-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "order-theory.large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06587701669662775 shape=circle style=filled width=0.06587701669662775] + "ring-theory.poset-of-right-ideals-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "order-theory.large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] + "ring-theory.poset-of-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06923831664020327 shape=circle style=filled width=0.06923831664020327] + "ring-theory.powers-of-elements-rings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "elementary-number-theory.parity-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "ring-theory.central-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "foundation.empty-types" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.powers-of-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.060901553009402865 shape=circle style=filled 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"ring-theory.precategory-of-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.precategory-of-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.precategory-of-semirings" -> "category-theory.large-precategories" [arrowhead=none color="#1A127710"] + "ring-theory.precategory-of-semirings" -> "category-theory.precategories" [arrowhead=none color="#1A127710"] + "ring-theory.precategory-of-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.precategory-of-semirings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] + "ring-theory.products-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" -> "ring-theory.ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "ring-theory.products-left-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" -> "ring-theory.left-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" -> "ring-theory.poset-of-left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] + "ring-theory.products-right-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" -> "ring-theory.right-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" -> "ring-theory.poset-of-right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06587701669662775 shape=circle style=filled width=0.06587701669662775] + "ring-theory.products-rings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.products-rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.products-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.products-rings" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#1A127710"] + "ring-theory.products-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06795090495055724 shape=circle style=filled width=0.06795090495055724] + "ring-theory.products-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.products-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.products-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.quotient-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.quotient-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.quotient-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.quotient-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.radical-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] + "ring-theory.radical-ideals-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.radical-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.radical-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12086734486480535 shape=circle style=filled width=0.12086734486480535] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "lists.concatenation-lists" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "ring-theory.poset-of-right-ideals-rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "lists.functoriality-lists" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "lists.lists" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-generated-by-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] + "ring-theory.right-ideals-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.right-ideals-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.1827046590282086 shape=circle style=filled width=0.1827046590282086] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.ring-of-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.multiplication-integer-fractions" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "foundation.contractible-types" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.unit-fractions-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.addition-integer-fractions" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.reduced-integer-fractions" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.multiplication-rational-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.multiplication-positive-and-negative-integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.positive-integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "ring-theory.localizations-rings" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "elementary-number-theory.integer-fractions" [arrowhead=none color="#1A127710"] + "ring-theory.ring-extensions-rational-numbers" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.1336553442676484 shape=circle style=filled width=0.1336553442676484] + "ring-theory.rings" -> "lists.concatenation-lists" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.involutions" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.embeddings" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.binary-equivalences" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.injective-maps" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.binary-embeddings" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.negation" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "lists.lists" [arrowhead=none color="#1A127710"] + "ring-theory.rings" -> "foundation.unital-binary-operations" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.10021004013899694 shape=circle style=filled width=0.10021004013899694] + "ring-theory.semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "group-theory.monoids" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "foundation.negation" [arrowhead=none color="#1A127710"] + "ring-theory.semirings" -> "foundation.unital-binary-operations" [arrowhead=none color="#1A127710"] + "ring-theory.subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06942028362060094 shape=circle style=filled width=0.06942028362060094] + "ring-theory.subsets-rings" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#1A127710"] + "ring-theory.subsets-rings" -> "foundation.propositional-extensionality" [arrowhead=none color="#1A127710"] + "ring-theory.subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.subsets-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05814630195131898 shape=circle style=filled width=0.05814630195131898] + "ring-theory.subsets-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] + "ring-theory.subsets-semirings" -> "foundation.propositional-extensionality" 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"univalent-combinatorics.finite-types" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-families-of-elements-rings" -> "foundation.empty-types" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-families-of-elements-rings" -> "univalent-combinatorics.counting" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-families-of-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.09662078510538938 shape=circle style=filled width=0.09662078510538938] + "ring-theory.sums-of-finite-families-of-elements-semirings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-families-of-elements-semirings" -> "group-theory.sums-of-finite-families-of-elements-commutative-monoids" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-families-of-elements-semirings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#1A127710"] + 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"univalent-combinatorics.standard-finite-types" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-sequences-of-elements-rings" -> "linear-algebra.left-modules-rings" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-sequences-of-elements-rings" -> "linear-algebra.linear-maps-left-modules-rings" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-sequences-of-elements-rings" -> "lists.finite-sequences" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-sequences-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] + "ring-theory.sums-of-finite-sequences-of-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08758031277559175 shape=circle style=filled width=0.08758031277559175] + "ring-theory.sums-of-finite-sequences-of-elements-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] + 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color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.univalence" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "species.species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] + "species.cauchy-products-species-of-types-in-subuniverses" -> "foundation.coproduct-decompositions" [arrowhead=none color="#EDA55F10"] + 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shape=circle style=filled width=0.08929214202502928] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.pi-decompositions" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.pi-decompositions-subuniverse" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.global-subuniverses" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.coproducts-species-of-types" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.coproducts-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.product-decompositions" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.dirichlet-products-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] + "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.univalence" [arrowhead=none color="#EDA55F10"] + 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"foundation.contractible-types" [arrowhead=none color="#EDA55F10"] + "species.unit-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] + "species.unit-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.global-subuniverses" [arrowhead=none color="#EDA55F10"] + "species.unit-cauchy-composition-species-of-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] + "species.unit-cauchy-composition-species-of-types" -> "species.species-of-types" [arrowhead=none color="#EDA55F10"] + "species.unit-cauchy-composition-species-of-types" -> "foundation.contractible-types" [arrowhead=none color="#EDA55F10"] + "species.unlabeled-structures-species" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] + "species.unlabeled-structures-species" -> "species.species-of-types" [arrowhead=none color="#EDA55F10"] + "species.unlabeled-structures-species" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#EDA55F10"] + "structured-types.cartesian-products-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.cartesian-products-types-equipped-with-endomorphisms" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#069F6E10"] + "structured-types.cartesian-products-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.central-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.central-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09517369363237901 shape=circle style=filled width=0.09517369363237901] + "structured-types.commuting-squares-of-pointed-maps" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-triangles-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05479528381785756 shape=circle style=filled width=0.05479528381785756] + "structured-types.commuting-triangles-of-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-triangles-of-pointed-maps" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-triangles-of-pointed-maps" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.commuting-triangles-of-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.052442447127525396 shape=circle style=filled width=0.052442447127525396] + "structured-types.conjugation-pointed-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" -> "synthetic-homotopy-theory.functoriality-loop-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" -> "synthetic-homotopy-theory.conjugation-loops" [arrowhead=none color="#069F6E10"] + "structured-types.conjugation-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.constant-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.constant-pointed-maps" -> "foundation.constant-maps" [arrowhead=none color="#069F6E10"] + "structured-types.constant-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.constant-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.contractible-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.contractible-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.contractible-pointed-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.cyclic-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] + "structured-types.cyclic-types" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.cyclic-types" -> "foundation.surjective-maps" [arrowhead=none color="#069F6E10"] + "structured-types.cyclic-types" -> "foundation.iterating-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.cyclic-types" -> "structured-types.sets-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] + "structured-types.dependent-products-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-h-spaces" -> "structured-types.dependent-products-pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.dependent-products-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05814630195131898 shape=circle style=filled width=0.05814630195131898] + "structured-types.dependent-products-wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-wild-monoids" -> "structured-types.dependent-products-h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-products-wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06776499241351715 shape=circle style=filled width=0.06776499241351715] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.equivalence-extensionality" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.dependent-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07830199672637511 shape=circle style=filled width=0.07830199672637511] + "structured-types.equivalences-h-spaces" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "structured-types.morphisms-h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] + "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" -> "foundation.equivalences-arrows" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.089855504976604 shape=circle style=filled width=0.089855504976604] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.equivalence-extensionality" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.morphisms-types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.equivalences-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09437501914625597 shape=circle style=filled width=0.09437501914625597] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.subtype-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "structured-types.morphisms-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.equivalences-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.faithful-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.faithful-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.faithful-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.faithful-pointed-maps" -> "foundation.faithful-maps" [arrowhead=none color="#069F6E10"] + "structured-types.fibers-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.fibers-of-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.fibers-of-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.fibers-of-pointed-maps" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.finite-multiplication-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.finite-multiplication-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.finite-multiplication-magmas" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#069F6E10"] + "structured-types.finite-multiplication-magmas" -> "univalent-combinatorics.counting" [arrowhead=none color="#069F6E10"] + "structured-types.function-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.function-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.function-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.function-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] + "structured-types.function-h-spaces" -> "structured-types.dependent-products-h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.function-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.function-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.function-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.function-wild-monoids" -> "structured-types.dependent-products-wild-monoids" [arrowhead=none color="#069F6E10"] + "structured-types.function-wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.function-wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.function-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07068093650719452 shape=circle style=filled width=0.07068093650719452] + "structured-types.h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation-core.endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "structured-types.noncoherent-h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] + "structured-types.initial-pointed-type-equipped-with-automorphism" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08375140434156425 shape=circle style=filled width=0.08375140434156425] + "structured-types.initial-pointed-type-equipped-with-automorphism" -> "elementary-number-theory.integers" [arrowhead=none color="#069F6E10"] + "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.iterating-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.initial-pointed-type-equipped-with-automorphism" -> "structured-types.pointed-types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07973885045884406 shape=circle style=filled width=0.07973885045884406] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.symmetric-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "structured-types.constant-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.constant-maps" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.binary-transport" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-type-of-h-space-structures" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.involutive-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.involutive-types" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "lists.lists" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "structured-types.cartesian-products-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-pointed-cartesian-product-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.iterated-pointed-cartesian-product-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-pointed-cartesian-product-types" -> "lists.lists" [arrowhead=none color="#069F6E10"] + "structured-types.iterated-pointed-cartesian-product-types" -> "structured-types.pointed-cartesian-product-types" [arrowhead=none color="#069F6E10"] + "structured-types.magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.magmas" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] + "structured-types.medial-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] + "structured-types.medial-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.medial-magmas" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.medial-magmas" -> "structured-types.morphisms-magmas" [arrowhead=none color="#069F6E10"] + "structured-types.medial-magmas" -> "structured-types.product-magmas" [arrowhead=none color="#069F6E10"] + "structured-types.medial-magmas" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06192863306205975 shape=circle style=filled width=0.06192863306205975] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.subtype-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "structured-types.equivalences-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08999579468728597 shape=circle style=filled width=0.08999579468728597] + "structured-types.morphisms-h-spaces" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.morphisms-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.11790860453923727 shape=circle style=filled width=0.11790860453923727] + "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.whiskering-pointed-2-homotopies-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.morphisms-arrows" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation-core.homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-squares-of-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-twisted-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] + "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-twisted-pointed-arrows" -> "foundation.morphisms-twisted-arrows" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05943383002455521 shape=circle style=filled width=0.05943383002455521] + "structured-types.morphisms-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-automorphisms" -> "structured-types.morphisms-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05195909628863885 shape=circle style=filled width=0.05195909628863885] + "structured-types.morphisms-wild-monoids" -> "structured-types.morphisms-h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-wild-monoids" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] + "structured-types.morphisms-wild-monoids" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] + "structured-types.noncoherent-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.noncoherent-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] + "structured-types.noncoherent-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.opposite-pointed-spans" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.opposite-pointed-spans" -> "structured-types.pointed-spans" [arrowhead=none color="#069F6E10"] + "structured-types.opposite-pointed-spans" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.12221670009868099 shape=circle style=filled width=0.12221670009868099] + "structured-types.pointed-2-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.uniform-pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-2-homotopies" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-cartesian-product-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] + "structured-types.pointed-cartesian-product-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-cartesian-product-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-cartesian-product-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-dependent-functions" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-dependent-functions" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-dependent-functions" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-dependent-pair-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-dependent-pair-types" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.14162935078056077 shape=circle style=filled width=0.14162935078056077] + "structured-types.pointed-equivalences" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.injective-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.universal-property-pointed-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.sections" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.embeddings" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.pointed-retractions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.contractible-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.precomposition-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.retractions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-equivalences" -> "structured-types.postcomposition-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-families-of-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-families-of-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.12273173272218177 shape=circle style=filled width=0.12273173272218177] + "structured-types.pointed-homotopies" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09881552504494161 shape=circle style=filled width=0.09881552504494161] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.logical-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-retractions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.contractible-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.retractions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-isomorphisms" -> "foundation.sections" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] + "structured-types.pointed-maps" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-maps" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-maps" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-maps" -> "foundation.constant-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] + "structured-types.pointed-retractions" -> "foundation-core.contractible-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "foundation-core.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "foundation-core.retractions" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-retractions" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-sections" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-sections" -> "foundation.sections" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-sections" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-sections" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-sections" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08083874863001829 shape=circle style=filled width=0.08083874863001829] + "structured-types.pointed-span-diagrams" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-span-diagrams" -> "structured-types.pointed-spans" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-span-diagrams" -> "structured-types.morphisms-pointed-arrows" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-span-diagrams" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-spans" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] + "structured-types.pointed-spans" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-spans" -> "foundation.spans" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-spans" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-unit-type" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.pointed-unit-type" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-unit-type" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-unit-type" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] + "structured-types.pointed-universal-property-contractible-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.pointed-universal-property-contractible-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.postcomposition-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.postcomposition-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.postcomposition-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.precomposition-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.precomposition-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.precomposition-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.product-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.product-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.sets-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.sets-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.small-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] + "structured-types.small-pointed-types" -> "foundation.small-types" [arrowhead=none color="#069F6E10"] + "structured-types.small-pointed-types" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.small-pointed-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] + "structured-types.small-pointed-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.small-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-elements-involutive-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.symmetric-elements-involutive-types" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-elements-involutive-types" -> "structured-types.involutive-types" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.symmetric-h-spaces" -> "structured-types.symmetric-elements-involutive-types" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-h-spaces" -> "foundation.symmetric-operations" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-h-spaces" -> "structured-types.involutive-type-of-h-space-structures" [arrowhead=none color="#069F6E10"] + "structured-types.symmetric-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.transposition-pointed-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.transposition-pointed-span-diagrams" -> "structured-types.pointed-span-diagrams" [arrowhead=none color="#069F6E10"] + "structured-types.transposition-pointed-span-diagrams" -> "structured-types.opposite-pointed-spans" [arrowhead=none color="#069F6E10"] + "structured-types.types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.types-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.types-equipped-with-endomorphisms" -> "foundation.endomorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08943331546025578 shape=circle style=filled width=0.08943331546025578] + "structured-types.uniform-pointed-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] + "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.universal-property-pointed-equivalences" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.universal-property-pointed-equivalences" -> "structured-types.precomposition-pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.universal-property-pointed-equivalences" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.universal-property-pointed-equivalences" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.unpointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.unpointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08405212848450323 shape=circle style=filled width=0.08405212848450323] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.whiskering-homotopies-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09596572138218783 shape=circle style=filled width=0.09596572138218783] + "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09410728805605297 shape=circle style=filled width=0.09410728805605297] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.discrete-reflexive-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.uniform-pointed-homotopies" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.large-transitive-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "wild-category-theory.noncoherent-omega-precategories" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.transitive-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "wild-category-theory.noncoherent-large-omega-precategories" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.large-reflexive-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-category-of-pointed-types" -> "globular-types.large-globular-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-groups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.wild-groups" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.wild-groups" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] + "structured-types.wild-loops" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" -> "structured-types.wild-quasigroups" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.wild-loops" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07416481997178037 shape=circle style=filled width=0.07416481997178037] + "structured-types.wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] + "structured-types.wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] + "structured-types.wild-quasigroups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.wild-quasigroups" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] + "structured-types.wild-quasigroups" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "structured-types.wild-quasigroups" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] + "structured-types.wild-semigroups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] + "structured-types.wild-semigroups" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] + "synthetic-category-theory.cone-diagrams-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.12262889924562415 shape=circle style=filled width=0.12262889924562415] + "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] + "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "synthetic-category-theory.cospans-synthetic-categories" [arrowhead=none color="#2FEABE10"] + "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] + 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"trees.functoriality-fiber-directed-tree" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-fiber-directed-tree" -> "trees.equivalences-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.06663862600647072 shape=circle style=filled width=0.06663862600647072] + "trees.functoriality-w-types" -> "foundation.truncation-levels" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.fibers-of-maps" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.embeddings" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.contractible-maps" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.truncated-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.truncated-maps" [arrowhead=none color="#0F1D6910"] + "trees.functoriality-w-types" -> "foundation.propositional-maps" [arrowhead=none color="#0F1D6910"] + "trees.hereditary-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.09410728805605297 shape=circle style=filled width=0.09410728805605297] + "trees.hereditary-w-types" -> "trees.binary-w-types" [arrowhead=none color="#0F1D6910"] + "trees.hereditary-w-types" -> "foundation.retractions" [arrowhead=none color="#0F1D6910"] + "trees.hereditary-w-types" -> "foundation.sections" [arrowhead=none color="#0F1D6910"] + "trees.hereditary-w-types" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#0F1D6910"] + "trees.indexed-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.induction-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] + "trees.induction-w-types" -> "foundation.negation" [arrowhead=none color="#0F1D6910"] + "trees.induction-w-types" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.induction-w-types" -> "trees.inequality-w-types" [arrowhead=none color="#0F1D6910"] + "trees.induction-w-types" -> "trees.elementhood-relation-w-types" [arrowhead=none color="#0F1D6910"] + "trees.inequality-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" 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"trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.homotopy-induction" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-coalgebras-polynomial-endofunctors" -> "foundation.torsorial-type-families" [arrowhead=none color="#0F1D6910"] + "trees.morphisms-directed-trees" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.08815461606208143 shape=circle style=filled width=0.08815461606208143] + 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"trees.full-binary-trees" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "foundation.sections" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "lists.lists" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "foundation.maybe" [arrowhead=none color="#0F1D6910"] + "trees.plane-trees" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#0F1D6910"] + "trees.polynomial-endofunctors" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.06373568211054055 shape=circle style=filled width=0.06373568211054055] + "trees.polynomial-endofunctors" -> "foundation.structure-identity-principle" [arrowhead=none color="#0F1D6910"] + "trees.polynomial-endofunctors" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + 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"trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.small-multisets" -> "foundation.univalence" [arrowhead=none color="#0F1D6910"] + "trees.submultisets" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.submultisets" -> "trees.multisets" [arrowhead=none color="#0F1D6910"] + "trees.submultisets" -> "foundation.embeddings" [arrowhead=none color="#0F1D6910"] + "trees.transitive-multisets" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.transitive-multisets" -> "trees.submultisets" [arrowhead=none color="#0F1D6910"] + "trees.transitive-multisets" -> "trees.multisets" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.1549844670585943 shape=circle style=filled width=0.1549844670585943] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.coalgebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "graph-theory.directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.equivalences-enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.isolated-elements" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.equivalences-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.equivalence-extensionality" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.binary-transport" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "graph-theory.morphisms-directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.negated-equality" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.elementhood-relation-coalgebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "graph-theory.walks-directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.combinator-enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "trees.combinator-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.empty-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.torsorial-type-families" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.10936009300072398 shape=circle style=filled width=0.10936009300072398] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.elementhood-relation-w-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "graph-theory.directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.equivalences-enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.isolated-elements" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.equivalences-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.equivalence-extensionality" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "graph-theory.morphisms-directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.underlying-trees-elements-coalgebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.negated-equality" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "graph-theory.walks-directed-graphs" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.combinator-enriched-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "trees.combinator-directed-trees" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.empty-types" [arrowhead=none color="#0F1D6910"] + "trees.underlying-trees-of-elements-of-w-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.102819789765237 shape=circle style=filled width=0.102819789765237] + "trees.undirected-trees" -> "graph-theory.trails-undirected-graphs" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "graph-theory.paths-undirected-graphs" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "foundation.decidable-types" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "foundation.decidable-equality" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "foundation.mere-equality" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "graph-theory.walks-undirected-graphs" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "foundation.empty-types" [arrowhead=none color="#0F1D6910"] + "trees.undirected-trees" -> "graph-theory.undirected-graphs" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.universal-multiset" -> "foundation.small-types" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "trees.small-multisets" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "foundation.small-universes" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "foundation.raising-universe-levels" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "trees.multisets" [arrowhead=none color="#0F1D6910"] + "trees.universal-multiset" -> "trees.functoriality-w-types" [arrowhead=none color="#0F1D6910"] + "trees.universal-tree" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.w-type-of-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] + "trees.w-type-of-natural-numbers" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-natural-numbers" -> "foundation.booleans" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-natural-numbers" -> "foundation.universal-property-empty-type" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-natural-numbers" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-propositions" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.05 shape=circle style=filled width=0.05] + "trees.w-type-of-propositions" -> "foundation.propositional-extensionality" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-propositions" -> "trees.w-types" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-propositions" -> "trees.extensional-w-types" [arrowhead=none color="#0F1D6910"] + "trees.w-type-of-propositions" -> "foundation.empty-types" [arrowhead=none color="#0F1D6910"] + "trees.w-types" [label="" color="#FFFFFF00" fillcolor="#0F1D69" height=0.09596572138218783 shape=circle style=filled width=0.09596572138218783] + "trees.w-types" -> "foundation.truncation-levels" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "trees.morphisms-algebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "trees.algebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "trees.coalgebras-polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "trees.polynomial-endofunctors" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.contractible-types" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.truncated-types" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.postcomposition-functions" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.homotopy-induction" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.empty-types" [arrowhead=none color="#0F1D6910"] + "trees.w-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#0F1D6910"] + "type-theories.comprehension-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.05 shape=circle style=filled width=0.05] + "type-theories.dependent-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.20104855494778812 shape=circle style=filled width=0.20104855494778812] + "type-theories.dependent-type-theories" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#610CCA10"] + "type-theories.dependent-type-theories" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#610CCA10"] + "type-theories.fibered-dependent-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.13774588077438535 shape=circle style=filled width=0.13774588077438535] + "type-theories.fibered-dependent-type-theories" -> "type-theories.dependent-type-theories" [arrowhead=none color="#610CCA10"] + "type-theories.pi-types-precategories-with-attributes" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.05 shape=circle style=filled width=0.05] + "type-theories.pi-types-precategories-with-attributes" -> "type-theories.precategories-with-attributes" [arrowhead=none color="#610CCA10"] + "type-theories.pi-types-precategories-with-families" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.05 shape=circle style=filled width=0.05] + "type-theories.pi-types-precategories-with-families" -> "type-theories.precategories-with-families" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.07450424883882695 shape=circle style=filled width=0.07450424883882695] + "type-theories.precategories-with-attributes" -> "category-theory.presheaf-categories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "foundation.category-of-sets" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.commuting-squares-of-morphisms-in-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.precategory-of-elements-of-a-presheaf" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.functors-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.pullbacks-in-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.natural-transformations-functors-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "foundation.sections" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-attributes" -> "category-theory.opposite-precategories" [arrowhead=none 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"category-theory.natural-transformations-functors-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-families" -> "foundation.sections" [arrowhead=none color="#610CCA10"] + "type-theories.precategories-with-families" -> "category-theory.opposite-precategories" [arrowhead=none color="#610CCA10"] + "type-theories.sections-dependent-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.06720416904044836 shape=circle style=filled width=0.06720416904044836] + "type-theories.sections-dependent-type-theories" -> "type-theories.dependent-type-theories" [arrowhead=none color="#610CCA10"] + "type-theories.sections-dependent-type-theories" -> "type-theories.fibered-dependent-type-theories" [arrowhead=none color="#610CCA10"] + "type-theories.simple-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.13627262043998845 shape=circle style=filled width=0.13627262043998845] + "type-theories.simple-type-theories" -> "type-theories.dependent-type-theories" [arrowhead=none color="#610CCA10"] + "type-theories.simple-type-theories" -> "type-theories.fibered-dependent-type-theories" [arrowhead=none color="#610CCA10"] + "type-theories.unityped-type-theories" [label="" color="#FFFFFF00" fillcolor="#610CCA" height=0.11005006888639714 shape=circle style=filled width=0.11005006888639714] + "type-theories.unityped-type-theories" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#610CCA10"] + "univalent-combinatorics.2-element-decidable-subtypes" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.11186920152852965 shape=circle style=filled width=0.11186920152852965] + "univalent-combinatorics.2-element-decidable-subtypes" -> "univalent-combinatorics.dependent-function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.logical-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "univalent-combinatorics.2-element-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.decidable-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.decidable-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.negation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.decidable-propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "foundation.mere-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.2-element-decidable-subtypes" -> 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"univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "lists.sort-by-insertion-lists" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "elementary-number-theory.fundamental-theorem-of-arithmetic" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "group-theory.concrete-groups" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> "lists.arrays" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.cycle-prime-decomposition-natural-numbers" -> 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"univalent-combinatorics.decidable-subtypes" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.decidable-subtypes" -> "univalent-combinatorics.function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.decidable-subtypes" -> "foundation.decidable-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.decidable-subtypes" -> "univalent-combinatorics.decidable-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.decidable-subtypes" -> "foundation.decidable-propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.decidable-subtypes" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.dedekind-finite-sets" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.dedekind-finite-sets" -> 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"univalent-combinatorics.main-classes-of-latin-hypercubes" -> "univalent-combinatorics.truncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "univalent-combinatorics.untruncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "foundation.set-truncations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "foundation.decidable-propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "foundation.mere-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-hypercubes" -> "foundation.inhabited-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.main-classes-of-latin-squares" -> "univalent-combinatorics.untruncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "foundation.set-truncations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "foundation.1-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "foundation.mere-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "univalent-combinatorics.main-classes-of-latin-hypercubes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.main-classes-of-latin-squares" -> "univalent-combinatorics.truncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.maybe" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.maybe" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.maybe" -> "foundation.maybe" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.maybe" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.necklaces" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.058362862484713576 shape=circle style=filled width=0.058362862484713576] + "univalent-combinatorics.necklaces" -> "foundation.structure-identity-principle" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.necklaces" -> "univalent-combinatorics.cyclic-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.necklaces" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.necklaces" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.necklaces" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.3 shape=circle style=filled width=0.3] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.congruence-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.logical-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.equivalence-classes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.intersections-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.equivalence-extensionality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.decidable-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.negation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.decidable-propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.mere-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.symmetric-difference" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.modular-arithmetic-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.2-element-decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "finite-group-theory.transpositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.involutions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.decidable-equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "foundation.iterating-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.orientations-cubes" -> "univalent-combinatorics.cubes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.08099465764396384 shape=circle style=filled width=0.08099465764396384] + "univalent-combinatorics.partitions" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.structure-identity-principle" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.binary-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.partitions" -> "foundation.equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.petri-nets" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.petri-nets" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.08671172622602275 shape=circle style=filled width=0.08671172622602275] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.dependent-function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.existential-quantification" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.maybe" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.truncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.untruncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.set-truncations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.retracts-of-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.dependent-function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.equality-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.finitely-truncated-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.truncation-levels" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.retracts-of-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.finitely-many-connected-components" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.conjunction" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.unbounded-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pi-finite-types" -> "foundation.truncated-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.09970520045352134 shape=circle style=filled width=0.09970520045352134] + "univalent-combinatorics.pigeonhole-principle" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.embeddings-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.noninjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.negation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.repetitions-of-values" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.pairs-of-distinct-elements" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.presented-pi-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.quotients-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.quotients-finite-types" -> "univalent-combinatorics.image-of-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.quotients-finite-types" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.quotients-finite-types" -> "univalent-combinatorics.decidable-equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.quotients-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.ramsey-theory" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.ramsey-theory" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.ramsey-theory" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values-sequences" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.repetitions-of-values" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.counting-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.counting-decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.decidable-dependent-function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.repetitions-of-values" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.decidable-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.noninjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.negation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.decidable-propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "foundation.pairs-of-distinct-elements" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.decidable-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "elementary-number-theory.well-ordering-principle-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.repetitions-of-values" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.fibers-of-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.counting-decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.retractions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.decidable-embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.retracts-of-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "foundation.decidable-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.retracts-of-finite-types" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.riffle-shuffles" -> "foundation.automorphisms" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "foundation-core.coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "elementary-number-theory.inequality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "foundation.conjunction" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "foundation-core.propositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.riffle-shuffles" -> "order-theory.posets" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] + "univalent-combinatorics.sequences-finite-types" -> "elementary-number-theory.well-ordering-principle-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "lists.sequences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "lists.repetitions-sequences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "foundation.repetitions-of-values" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "foundation.pairs-of-distinct-elements" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "elementary-number-theory.decidable-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "univalent-combinatorics.pigeonhole-principle" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sequences-finite-types" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.logical-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.set-quotients-of-index-two" -> "foundation.equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.11073574573133337 shape=circle style=filled width=0.11073574573133337] + "univalent-combinatorics.sigma-decompositions" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.logical-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.precomposition-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "univalent-combinatorics.type-duality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "univalent-combinatorics.decidable-equivalence-relations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "univalent-combinatorics.inhabited-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.surjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.sigma-decompositions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sigma-decompositions" -> "foundation.inhabited-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.skipping-element-standard-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.skipping-element-standard-finite-types" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.skipping-element-standard-finite-types" -> "foundation.equality-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.skipping-element-standard-finite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.skipping-element-standard-finite-types" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.small-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.small-types" -> "foundation.small-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.small-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.small-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-pruned-trees" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.standard-finite-pruned-trees" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-trees" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.standard-finite-trees" -> "elementary-number-theory.sums-of-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-trees" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-trees" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-trees" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.11321437051972819 shape=circle style=filled width=0.11321437051972819] + "univalent-combinatorics.standard-finite-types" -> "foundation.equivalences-maybe" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.raising-universe-levels" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.preunivalent-type-families" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.decidable-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.negation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.equality-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.sections" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.noncontractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.retractions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "foundation.equivalence-injective-type-families" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.standard-finite-types" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.steiner-systems" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.steiner-systems" -> "foundation.decidable-subtypes" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.steiner-systems" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.steiner-systems" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.steiner-triple-systems" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.steiner-triple-systems" -> "univalent-combinatorics.steiner-systems" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.08479927320887588 shape=circle style=filled width=0.08479927320887588] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "univalent-combinatorics.sequences-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.minimum-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.nonzero-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.split-surjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.repetitions-of-values" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.decidable-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.empty-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "foundation.iterating-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subcounting" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.10536491916228899 shape=circle style=filled width=0.10536491916228899] + "univalent-combinatorics.subfinite-indexing" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "univalent-combinatorics.dedekind-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.fibers-of-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "elementary-number-theory.nonzero-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.iterating-functions" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.repetitions-of-values" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.retracts-of-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.surjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "univalent-combinatorics.pigeonhole-principle" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "foundation.propositional-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "univalent-combinatorics.finite-choice" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "univalent-combinatorics.subcounting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-indexing" -> "elementary-number-theory.minimum-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.06813631021999422 shape=circle style=filled width=0.06813631021999422] + "univalent-combinatorics.subfinite-types" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "foundation.decidable-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "univalent-combinatorics.dedekind-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "foundation.discrete-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "univalent-combinatorics.subcounting" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinite-types" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.subfinite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.dedekind-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "foundation.existential-quantification" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "foundation.embeddings" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.image-of-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "foundation.decidable-equality" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "foundation.surjective-maps" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.subfinitely-enumerable-types" -> "univalent-combinatorics.subfinite-indexing" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sums-of-natural-numbers" [label="" color="#FFFFFF00" fillcolor="#F70D61" height=0.05 shape=circle style=filled width=0.05] + "univalent-combinatorics.sums-of-natural-numbers" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sums-of-natural-numbers" -> "elementary-number-theory.sums-of-natural-numbers" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.sums-of-natural-numbers" -> "univalent-combinatorics.counting-dependent-pair-types" [arrowhead=none 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color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "univalent-combinatorics.untruncated-pi-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "univalent-combinatorics.function-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "foundation.set-truncations" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "foundation.retracts-of-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "foundation.equality-coproduct-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] + "univalent-combinatorics.unbounded-pi-finite-types" -> 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height=0.05 shape=circle style=filled width=0.05] + "universal-algebra.algebraic-theories" -> "universal-algebra.signatures" [arrowhead=none color="#5467C310"] + "universal-algebra.algebraic-theories" -> "universal-algebra.abstract-equations-over-signatures" [arrowhead=none color="#5467C310"] + "universal-algebra.algebraic-theory-of-groups" [label="" color="#FFFFFF00" fillcolor="#5467C3" height=0.0647177997777583 shape=circle style=filled width=0.0647177997777583] + "universal-algebra.algebraic-theory-of-groups" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#5467C310"] + "universal-algebra.algebraic-theory-of-groups" -> "universal-algebra.signatures" [arrowhead=none color="#5467C310"] + "universal-algebra.algebraic-theory-of-groups" -> "universal-algebra.terms-over-signatures" [arrowhead=none color="#5467C310"] + "universal-algebra.algebraic-theory-of-groups" -> "group-theory.groups" [arrowhead=none color="#5467C310"] + 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"wild-category-theory.noncoherent-omega-precategories" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#E2C12E10"] + "wild-category-theory.noncoherent-omega-precategories" -> "globular-types.transitive-globular-types" [arrowhead=none color="#E2C12E10"] + "wild-category-theory.noncoherent-omega-precategories" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#E2C12E10"] + "wild-category-theory.noncoherent-omega-precategories" -> "category-theory.precategories" [arrowhead=none color="#E2C12E10"] + "wild-category-theory.noncoherent-omega-precategories" -> "globular-types.globular-types" [arrowhead=none color="#E2C12E10"] + "wild-category-theory.noncoherent-omega-precategories" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#E2C12E10"] +} From 9be2d1642c4fee4ffc3994133c0da7d85f075450 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:44:39 +0200 Subject: [PATCH 09/13] ?? --- website/images/agda_dependency_graph | 21264 ------------------------- 1 file changed, 21264 deletions(-) delete mode 100644 website/images/agda_dependency_graph diff --git a/website/images/agda_dependency_graph b/website/images/agda_dependency_graph deleted file mode 100644 index b9f2415197..0000000000 --- a/website/images/agda_dependency_graph +++ /dev/null @@ -1,21264 +0,0 @@ -digraph { - K=0.3 bgcolor="#FFFFFF00" overlap=prism10000 repulsiveforce=0.3 splines=false - "category-theory.adjunctions-large-categories" [label="" color="#FFFFFF00" fillcolor="#fbca04" height=0.1141023399696225 shape=circle style=filled width=0.1141023399696225] - "category-theory.adjunctions-large-categories" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#fbca0410"] - "category-theory.adjunctions-large-categories" -> "category-theory.adjunctions-large-precategories" [arrowhead=none color="#fbca0410"] - "category-theory.adjunctions-large-categories" -> "category-theory.large-categories" 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"commutative-algebra.binomial-theorem-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07121438510526466 shape=circle style=filled width=0.07121438510526466] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "linear-algebra.finite-sequences-in-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "ring-theory.binomial-theorem-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "commutative-algebra.powers-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.binomial-coefficients" [arrowhead=none color="#3577BB10"] - "commutative-algebra.binomial-theorem-commutative-semirings" -> "elementary-number-theory.distance-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.boolean-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.boolean-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.boolean-rings" -> "ring-theory.idempotent-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.category-of-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.category-of-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.category-of-commutative-rings" -> "category-theory.large-categories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.category-of-commutative-rings" -> "category-theory.categories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.category-of-commutative-rings" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.1296303861210299 shape=circle style=filled width=0.1296303861210299] - "commutative-algebra.commutative-rings" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.involutions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.binary-equivalences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.binary-embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.negation" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "lists.lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09124869666223606 shape=circle style=filled width=0.09124869666223606] - "commutative-algebra.commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-semirings" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-semirings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07846294652976578 shape=circle style=filled width=0.07846294652976578] - "commutative-algebra.convolution-sequences-commutative-rings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "lists.sequences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "commutative-algebra.convolution-sequences-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "commutative-algebra.function-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.11498345220469042 shape=circle style=filled width=0.11498345220469042] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "lists.sequences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.function-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "elementary-number-theory.binary-sum-decompositions-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.convolution-sequences-commutative-semirings" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0645225721843014 shape=circle style=filled width=0.0645225721843014] - "commutative-algebra.dependent-products-commutative-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" -> "group-theory.dependent-products-commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" -> "ring-theory.dependent-products-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06625891564490792 shape=circle style=filled width=0.06625891564490792] - "commutative-algebra.dependent-products-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-semirings" -> "group-theory.dependent-products-commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.dependent-products-commutative-semirings" -> "ring-theory.dependent-products-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.discrete-fields" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.discrete-fields" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.discrete-fields" -> "ring-theory.division-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.11694168394216668 shape=circle style=filled width=0.11694168394216668] - "commutative-algebra.eisenstein-integers" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.eisenstein-integers" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.13289808409807344 shape=circle style=filled width=0.13289808409807344] - "commutative-algebra.euclidean-domains" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "commutative-algebra.trivial-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.binary-embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.negation" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "lists.lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.involutions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.binary-equivalences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.euclidean-domains" -> "commutative-algebra.integral-domains" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07700228825802675 shape=circle style=filled width=0.07700228825802675] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "ring-theory.full-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.full-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06432675209026768 shape=circle style=filled width=0.06432675209026768] - "commutative-algebra.function-commutative-rings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-rings" -> "commutative-algebra.dependent-products-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06757856842230686 shape=circle style=filled width=0.06757856842230686] - "commutative-algebra.function-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-semirings" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-semirings" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.function-commutative-semirings" -> "commutative-algebra.dependent-products-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09609709135660312 shape=circle style=filled width=0.09609709135660312] - "commutative-algebra.gaussian-integers" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "elementary-number-theory.difference-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.gaussian-integers" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09069398819863565 shape=circle style=filled width=0.09069398819863565] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "category-theory.functors-large-precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "ring-theory.groups-of-units-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.submonoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.groups-of-units-commutative-rings" -> "group-theory.category-of-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.1060808838144246 shape=circle style=filled width=0.1060808838144246] - "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.invertible-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09907053327553424 shape=circle style=filled width=0.09907053327553424] - "commutative-algebra.homomorphisms-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-semirings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-semirings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-semirings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.homomorphisms-commutative-semirings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.08223128882139645 shape=circle style=filled width=0.08223128882139645] - "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] - "commutative-algebra.ideals-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-semirings" -> "commutative-algebra.subsets-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-commutative-semirings" -> "ring-theory.ideals-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "ring-theory.ideals-generated-by-subsets-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09410728805605297 shape=circle style=filled width=0.09410728805605297] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.multiples-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.multiplication-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integer-multiples-of-elements-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.12456821978060995 shape=circle style=filled width=0.12456821978060995] - "commutative-algebra.integral-domains" -> "lists.concatenation-lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.involutions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.interchange-law" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "commutative-algebra.trivial-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "group-theory.monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "ring-theory.semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.binary-equivalences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.injective-maps" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "group-theory.commutative-monoids" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.binary-embeddings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.negation" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "lists.lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.integral-domains" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05985685194678195 shape=circle style=filled width=0.05985685194678195] - "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "foundation.intersections-subtypes" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "ring-theory.intersections-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09124869666223606 shape=circle style=filled width=0.09124869666223606] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.products-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.full-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.intersections-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.intersections-radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.invertible-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09356952772180921 shape=circle style=filled width=0.09356952772180921] - "commutative-algebra.invertible-elements-commutative-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.invertible-elements-commutative-rings" -> "foundation.contractible-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.invertible-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.10738108802578482 shape=circle style=filled width=0.10738108802578482] - "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "category-theory.isomorphisms-in-large-precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "ring-theory.isomorphisms-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.invertible-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "group-theory.isomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "commutative-algebra.precategory-of-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.isomorphisms-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07942179611987281 shape=circle style=filled width=0.07942179611987281] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "ring-theory.joins-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.products-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.11769441979464867 shape=circle style=filled width=0.11769441979464867] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "order-theory.large-suplattices" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.joins-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.products-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.intersections-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.joins-radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.local-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.local-commutative-rings" -> "ring-theory.local-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.local-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.local-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.maximal-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.multiples-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05964571600864011 shape=circle style=filled width=0.05964571600864011] - "commutative-algebra.multiples-of-elements-commutative-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.multiples-of-elements-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.multiples-of-elements-commutative-rings" -> "ring-theory.multiples-of-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.multiples-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] - "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "ring-theory.nilpotent-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.prime-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradical-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradicals-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.nilradicals-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradicals-commutative-semirings" -> "commutative-algebra.subsets-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradicals-commutative-semirings" -> "ring-theory.nilpotent-elements-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.nilradicals-commutative-semirings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] - "commutative-algebra.poset-of-ideals-commutative-rings" -> "order-theory.large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-ideals-commutative-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-ideals-commutative-rings" -> "order-theory.large-preorders" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06960177486788897 shape=circle style=filled width=0.06960177486788897] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "order-theory.large-preorders" [arrowhead=none color="#3577BB10"] - "commutative-algebra.poset-of-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] - "commutative-algebra.powers-of-elements-commutative-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-rings" -> "elementary-number-theory.parity-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-rings" -> "ring-theory.powers-of-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.powers-of-elements-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.powers-of-elements-commutative-semirings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.precategory-of-commutative-rings" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-rings" -> "category-theory.large-precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-rings" -> "category-theory.precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.precategory-of-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-semirings" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-semirings" -> "category-theory.large-precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-semirings" -> "category-theory.precategories" [arrowhead=none color="#3577BB10"] - "commutative-algebra.precategory-of-commutative-semirings" -> "ring-theory.precategory-of-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "foundation.disjunction" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.full-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.prime-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07450424883882695 shape=circle style=filled width=0.07450424883882695] - "commutative-algebra.products-commutative-rings" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "group-theory.groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "ring-theory.products-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.12816227098468916 shape=circle style=filled width=0.12816227098468916] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "ring-theory.products-ideals-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.products-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "lists.lists" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.08223128882139645 shape=circle style=filled width=0.08223128882139645] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.products-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-subsets-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] - "commutative-algebra.products-subsets-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-subsets-commutative-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-subsets-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.products-subsets-commutative-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.07551338170027617 shape=circle style=filled width=0.07551338170027617] - "commutative-algebra.radical-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.05 shape=circle style=filled width=0.05] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.radicals-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.ideals-generated-by-subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.09027572007459915 shape=circle style=filled width=0.09027572007459915] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.subsets-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.poset-of-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.powers-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.poset-of-radical-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.binomial-theorem-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.radicals-of-ideals-commutative-rings" -> "commutative-algebra.ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06393331260689927 shape=circle style=filled width=0.06393331260689927] - "commutative-algebra.subsets-commutative-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-rings" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-rings" -> "foundation.propositional-extensionality" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] - "commutative-algebra.subsets-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.subsets-commutative-semirings" -> "ring-theory.subsets-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0760129244023573 shape=circle style=filled width=0.0760129244023573] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "foundation.automorphisms" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "finite-group-theory.permutations-standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "linear-algebra.finite-sequences-in-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "foundation.empty-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "ring-theory.sums-of-finite-families-of-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-rings" -> "univalent-combinatorics.counting" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.08005464912226617 shape=circle style=filled width=0.08005464912226617] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "foundation.automorphisms" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "finite-group-theory.permutations-standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "linear-algebra.finite-sequences-in-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "lists.finite-sequences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "foundation.empty-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "ring-theory.sums-of-finite-families-of-elements-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-families-of-elements-commutative-semirings" -> "univalent-combinatorics.counting" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.0792627933655572 shape=circle style=filled width=0.0792627933655572] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "finite-group-theory.permutations-standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "linear-algebra.finite-sequences-in-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "ring-theory.sums-of-finite-sequences-of-elements-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-rings" -> "lists.finite-sequences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.08130557877817587 shape=circle style=filled width=0.08130557877817587] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "linear-algebra.finite-sequences-in-commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "commutative-algebra.commutative-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "finite-group-theory.permutations-standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "ring-theory.sums-of-finite-sequences-of-elements-semirings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "univalent-combinatorics.coproduct-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.sums-of-finite-sequences-of-elements-commutative-semirings" -> "lists.finite-sequences" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.06432675209026768 shape=circle style=filled width=0.06432675209026768] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "group-theory.isomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "foundation.unital-binary-operations" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups" -> "commutative-algebra.homomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" [label="" color="#FFFFFF00" fillcolor="#3577BB" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] - "commutative-algebra.trivial-commutative-rings" -> "group-theory.trivial-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "foundation.negation" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "foundation.structure-identity-principle" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "ring-theory.trivial-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "foundation.contractible-types" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "commutative-algebra.isomorphisms-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.trivial-commutative-rings" -> "ring-theory.rings" [arrowhead=none color="#3577BB10"] - 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shape=circle style=filled width=0.05] - "commutative-algebra.zariski-topology" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.zariski-topology" -> "commutative-algebra.prime-ideals-commutative-rings" [arrowhead=none color="#3577BB10"] - "commutative-algebra.zariski-topology" -> "foundation.existential-quantification" [arrowhead=none color="#3577BB10"] - "domain-theory.directed-complete-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.06625891564490792 shape=circle style=filled width=0.06625891564490792] - "domain-theory.directed-complete-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] - "domain-theory.directed-complete-posets" -> "foundation.binary-relations" [arrowhead=none color="#FCBFF510"] - "domain-theory.directed-complete-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.directed-complete-posets" -> "order-theory.posets" 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color="#FCBFF510"] - "domain-theory.directed-families-posets" -> "foundation.inhabited-types" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.08758031277559175 shape=circle style=filled width=0.08758031277559175] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-complete-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.fixed-points-endofunctions" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.chains-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-continuous-maps-omega-complete-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "elementary-number-theory.decidable-total-order-natural-numbers" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "order-theory.posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.kleenes-fixed-point-theorem-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "domain-theory.omega-continuous-maps-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.kleenes-fixed-point-theorem-omega-complete-posets" -> "foundation.iterating-functions" [arrowhead=none color="#FCBFF510"] - 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width=0.10021004013899694] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "domain-theory.omega-complete-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.subtype-identity-principle" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.join-preserving-maps-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.existential-quantification" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.raising-universe-levels" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> 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"foundation.homotopy-induction" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.surjective-maps" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "domain-theory.directed-families-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "foundation.torsorial-type-families" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-omega-complete-posets" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#FCBFF510"] - "domain-theory.omega-continuous-maps-posets" [label="" color="#FFFFFF00" fillcolor="#FCBFF5" height=0.09701170019522755 shape=circle style=filled width=0.09701170019522755] - "domain-theory.omega-continuous-maps-posets" -> 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-> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#524F8810"] - "finite-algebra.homomorphisms-finite-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#524F8810"] - "finite-algebra.homomorphisms-finite-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.08553989227683015 shape=circle style=filled width=0.08553989227683015] - "finite-algebra.products-commutative-finite-rings" -> "group-theory.semigroups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "group-theory.groups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "commutative-algebra.products-commutative-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "finite-algebra.products-finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-commutative-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.07121438510526466 shape=circle style=filled width=0.07121438510526466] - "finite-algebra.products-finite-rings" -> "finite-algebra.finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "group-theory.semigroups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "group-theory.groups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "ring-theory.products-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "univalent-combinatorics.cartesian-product-types" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "ring-theory.rings" [arrowhead=none color="#524F8810"] - "finite-algebra.products-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" [label="" color="#FFFFFF00" fillcolor="#524F88" height=0.05 shape=circle style=filled width=0.05] - "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.dependent-products-commutative-finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.homomorphisms-commutative-finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.finite-fields" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "foundation.existential-quantification" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "finite-algebra.commutative-finite-rings" [arrowhead=none color="#524F8810"] - "finite-algebra.semisimple-commutative-finite-rings" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#524F8810"] - "finite-group-theory.abstract-quaternion-group" [label="" color="#FFFFFF00" fillcolor="#9A01E2" height=0.1540045765160535 shape=circle style=filled width=0.1540045765160535] - "finite-group-theory.abstract-quaternion-group" -> "group-theory.semigroups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "group-theory.groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "foundation.decidable-types" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "foundation.decidable-equality" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "foundation.negation" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "foundation.empty-types" [arrowhead=none color="#9A01E210"] - "finite-group-theory.abstract-quaternion-group" -> "univalent-combinatorics.counting" [arrowhead=none color="#9A01E210"] - "finite-group-theory.alternating-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#9A01E2" height=0.05 shape=circle style=filled width=0.05] - "finite-group-theory.alternating-concrete-groups" -> "group-theory.kernels-homomorphisms-concrete-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.alternating-concrete-groups" -> "finite-group-theory.finite-type-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.alternating-concrete-groups" -> "finite-group-theory.cartier-delooping-sign-homomorphism" [arrowhead=none color="#9A01E210"] - "finite-group-theory.alternating-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.alternating-groups" [label="" color="#FFFFFF00" fillcolor="#9A01E2" height=0.05 shape=circle style=filled width=0.05] - 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"group-theory.symmetric-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.mere-equivalences" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "finite-group-theory.delooping-sign-homomorphism" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.action-on-equivalences-type-families-over-subuniverses" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "group-theory.concrete-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.cartier-delooping-sign-homomorphism" -> "foundation.equivalence-relations" [arrowhead=none color="#9A01E210"] - "finite-group-theory.concrete-quaternion-group" [label="" color="#FFFFFF00" 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"finite-group-theory.transpositions" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "finite-group-theory.finite-type-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "group-theory.generating-sets-groups" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "finite-group-theory.permutations" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "foundation.binary-transport" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "foundation.empty-types" [arrowhead=none color="#9A01E210"] - "finite-group-theory.delooping-sign-homomorphism" -> "foundation.equivalence-induction" [arrowhead=none color="#9A01E210"] - 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shape=circle style=filled width=0.050978647882712] - "foundation-core.torsorial-type-families" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation-core.transport-along-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] - "foundation-core.truncated-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08700221858486124 shape=circle style=filled width=0.08700221858486124] - "foundation-core.truncated-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation-core.truncated-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation-core.truncated-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation-core.truncated-maps" -> "foundation.equality-fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation-core.truncated-maps" -> 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[arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation-core.retracts-of-types" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation-core.truncated-types" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation-core.truncation-levels" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - 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"foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation-core.universal-property-truncation" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation-core.whiskering-homotopies-concatenation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] - "foundation-core.whiskering-homotopies-concatenation" -> "foundation.whiskering-operations" [arrowhead=none color="#28453010"] - "foundation-core.whiskering-homotopies-concatenation" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] - "foundation-core.whiskering-homotopies-concatenation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation-core.whiskering-identifications-concatenation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09207449355456987 shape=circle style=filled width=0.09207449355456987] - "foundation-core.whiskering-identifications-concatenation" -> 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- "foundation.0-connected-types" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.set-truncations" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.images" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.fiber-inclusions" [arrowhead=none color="#28453010"] - "foundation.0-connected-types" -> "foundation.functoriality-set-truncation" [arrowhead=none color="#28453010"] - "foundation.0-images-of-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.0-images-of-maps" -> "foundation.truncation-images-of-maps" [arrowhead=none color="#28453010"] - "foundation.0-images-of-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.0-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0631390791325705 shape=circle style=filled width=0.0631390791325705] - "foundation.0-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.0-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.0-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.0-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.0-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.0-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.1-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] - "foundation.1-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation-core.1-types" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.1-types" -> "foundation.truncated-types" [arrowhead=none color="#28453010"] - "foundation.2-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.2-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.2-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions-out-of-subuniverses" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions-out-of-subuniverses" -> "foundation.equivalence-induction" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] - "foundation.action-on-equivalences-functions" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.action-on-equivalences-functions" -> 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"foundation.action-on-higher-identifications-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.action-on-higher-identifications-functions" -> "foundation.path-algebra" [arrowhead=none color="#28453010"] - "foundation.action-on-homotopies-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] - "foundation.action-on-homotopies-functions" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.action-on-homotopies-functions" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] - "foundation.action-on-homotopies-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.action-on-homotopies-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.action-on-homotopies-functions" -> "foundation.homotopy-induction" 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color="#28453010"] - "foundation.apartness-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07551338170027617 shape=circle style=filled width=0.07551338170027617] - "foundation.apartness-relations" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation.disjunction" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation.universal-quantification" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.apartness-relations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07534613148009645 shape=circle style=filled width=0.07534613148009645] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-coproduct-and-sigma-decompositions" -> "foundation.coproduct-decompositions" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07534613148009645 shape=circle style=filled width=0.07534613148009645] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.pi-decompositions" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.product-decompositions" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.arithmetic-law-product-and-pi-decompositions" -> "foundation.coproduct-decompositions" [arrowhead=none color="#28453010"] - "foundation.automorphisms" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.automorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] - "foundation.automorphisms" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.061108350049340496 shape=circle style=filled width=0.061108350049340496] - "foundation.axiom-of-choice" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.split-surjective-maps" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.projective-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "foundation.sections" [arrowhead=none color="#28453010"] - "foundation.axiom-of-choice" -> "univalent-combinatorics.counting" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06606824211104302 shape=circle style=filled width=0.06606824211104302] - "foundation.axiom-of-countable-choice" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.maybe" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.axiom-of-dependent-choice" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.decidable-equality" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "elementary-number-theory.equality-natural-numbers" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "univalent-combinatorics.classical-finite-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "set-theory.countable-sets" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-countable-choice" -> "foundation.axiom-of-choice" [arrowhead=none color="#28453010"] - "foundation.axiom-of-dependent-choice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.axiom-of-dependent-choice" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] - "foundation.axiom-of-dependent-choice" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.axiom-of-dependent-choice" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.axiom-of-dependent-choice" -> "foundation.axiom-of-choice" [arrowhead=none color="#28453010"] - "foundation.bands" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.bands" -> "foundation.set-truncations" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07313708225430403 shape=circle style=filled width=0.07313708225430403] - "foundation.base-changes-span-diagrams" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" -> "foundation.cartesian-morphisms-span-diagrams" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" -> "foundation.cartesian-morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.base-changes-span-diagrams" -> "foundation.morphisms-span-diagrams" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.bicomposition-functions" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation.postcomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.bicomposition-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.binary-dependent-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-dependent-identifications" -> "foundation.binary-transport" [arrowhead=none color="#28453010"] - "foundation.binary-embeddings" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-embeddings" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.binary-embeddings" -> "foundation.binary-equivalences" [arrowhead=none color="#28453010"] - "foundation.binary-embeddings" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#28453010"] - "foundation.binary-equivalences-unordered-pairs-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.products-unordered-pairs-of-types" [arrowhead=none color="#28453010"] - "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.binary-operations-unordered-pairs-of-types" [arrowhead=none color="#28453010"] - "foundation.binary-equivalences-unordered-pairs-of-types" -> "foundation.unordered-pairs" [arrowhead=none color="#28453010"] - "foundation.binary-equivalences" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-equivalences" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10993537362971544 shape=circle style=filled width=0.10993537362971544] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.exponents-set-quotients" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.set-quotients" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.binary-homotopies" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.binary-functoriality-set-quotients" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#28453010"] - "foundation.binary-homotopies" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-homotopies" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.binary-homotopies" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.binary-homotopies" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.binary-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.binary-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.binary-operations-unordered-pairs-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.binary-operations-unordered-pairs-of-types" -> "foundation.products-unordered-pairs-of-types" [arrowhead=none color="#28453010"] - "foundation.binary-operations-unordered-pairs-of-types" -> "foundation.unordered-pairs" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06131444962281207 shape=circle style=filled width=0.06131444962281207] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.equivalence-relations" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.binary-reflecting-maps-equivalence-relations" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-extensions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05857862241641752 shape=circle style=filled width=0.05857862241641752] - "foundation.binary-relations-with-extensions" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-extensions" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-extensions" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-lifts" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] - "foundation.binary-relations-with-lifts" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-lifts" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.binary-relations-with-lifts" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09957859062409573 shape=circle style=filled width=0.09957859062409573] - "foundation.binary-relations" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.binary-relations" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.binary-transport" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] - "foundation.binary-transport" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08269025771888006 shape=circle style=filled width=0.08269025771888006] - "foundation.binary-type-duality" -> "foundation.equivalences-spans" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation.retractions" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation.multivariable-homotopies" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation.spans" [arrowhead=none color="#28453010"] - "foundation.binary-type-duality" -> "foundation.sections" [arrowhead=none color="#28453010"] - "foundation.booleans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09289294959308962 shape=circle style=filled width=0.09289294959308962] - "foundation.booleans" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.involutions" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.decidable-propositions" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.discrete-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.decidable-equality" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.negated-equality" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.tight-apartness-relations" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#28453010"] - "foundation.booleans" -> "foundation.apartness-relations" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07330937243946685 shape=circle style=filled width=0.07330937243946685] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation.perfect-images" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation.split-surjective-maps" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation.law-of-excluded-middle" [arrowhead=none color="#28453010"] - "foundation.cantor-schroder-bernstein-escardo" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.cantors-theorem" [label="" color="#FFFFFF00" 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"foundation.commuting-triangles-of-homotopies" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-identifications" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.188013384631714 shape=circle style=filled width=0.188013384631714] - "foundation.commuting-triangles-of-identifications" -> "foundation-core.commuting-squares-of-identifications" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-identifications" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-identifications" -> "foundation.binary-equivalences" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08642025741401992 shape=circle style=filled width=0.08642025741401992] - "foundation.commuting-triangles-of-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation.homotopy-algebra" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-maps" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-morphisms-arrows" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.commuting-triangles-of-morphisms-arrows" -> "foundation.homotopies-morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.commuting-triangles-of-morphisms-arrows" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.complements-subtypes" -> "foundation.decidable-subtypes" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "logic.double-negation-stable-subtypes" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.opposite-large-posets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.unions-subtypes" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.full-subtypes" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.posets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.powersets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.large-posets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.negation" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.decidable-propositions" [arrowhead=none color="#28453010"] - "foundation.complements-subtypes" -> "foundation.double-negation-stable-propositions" [arrowhead=none color="#28453010"] - "foundation.complements" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.complements" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.composite-maps-in-inverse-sequential-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.composite-maps-in-inverse-sequential-diagrams" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#28453010"] - "foundation.composite-maps-in-inverse-sequential-diagrams" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] - "foundation.composite-maps-in-inverse-sequential-diagrams" -> "foundation.dependent-inverse-sequential-diagrams" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09041535777611572 shape=circle style=filled width=0.09041535777611572] - "foundation.composition-algebra" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" -> "foundation.whiskering-higher-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.composition-algebra" -> "foundation.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.composition-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06413033406810799 shape=circle style=filled width=0.06413033406810799] - "foundation.composition-spans" -> "foundation.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.equivalences-spans" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.pullbacks" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.equivalences-arrows" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.morphisms-spans" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.type-arithmetic-standard-pullbacks" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.composition-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.14331178406411677 shape=circle style=filled width=0.14331178406411677] - "foundation.computational-identity-types" -> "foundation.universal-property-identity-systems" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation.yoneda-identity-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.computational-identity-types" -> "foundation.strictly-right-unital-concatenation-identifications" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.12086734486480535 shape=circle style=filled width=0.12086734486480535] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.multivariable-homotopies" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.cones-over-cospan-diagrams" -> "foundation-core.whiskering-identifications-concatenation" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07050222336024897 shape=circle style=filled width=0.07050222336024897] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.binary-homotopies" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.cones-over-inverse-sequential-diagrams" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.conjunction" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07584677573504928 shape=circle style=filled width=0.07584677573504928] - "foundation.conjunction" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.conjunction" -> "foundation-core.decidable-propositions" [arrowhead=none color="#28453010"] - "foundation.conjunction" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.conjunction" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.conjunction" -> "foundation.universal-property-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.conjunction" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07032305604809001 shape=circle style=filled width=0.07032305604809001] - "foundation.connected-components-universes" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.raising-universe-levels" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.mere-equivalences" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.0-connected-types" [arrowhead=none color="#28453010"] - "foundation.connected-components-universes" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.connected-components" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] - "foundation.connected-components" -> "higher-group-theory.higher-groups" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation.0-connected-types" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.connected-components" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] - "foundation.connected-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.12180310601880573 shape=circle style=filled width=0.12180310601880573] - "foundation.connected-maps" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.precomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.universal-property-family-of-fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.connected-types" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.truncated-types" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.iterated-successors-truncation-levels" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.truncations" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.connected-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.connected-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08299482691834507 shape=circle style=filled width=0.08299482691834507] - "foundation.connected-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.retracts-of-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.functoriality-truncation" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.truncations" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.diagonal-maps-of-types" [arrowhead=none color="#28453010"] - "foundation.connected-types" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07226947050238228 shape=circle style=filled width=0.07226947050238228] - "foundation.constant-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.faithful-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.retracts-of-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.1-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.retracts-of-types" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.type-arithmetic-unit-type" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.action-on-homotopies-functions" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.0-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation.images" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.constant-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.constant-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.constant-span-diagrams" -> "foundation.span-diagrams" [arrowhead=none color="#28453010"] - "foundation.constant-span-diagrams" -> "foundation.spans" [arrowhead=none color="#28453010"] - "foundation.constant-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] - "foundation.constant-type-families" -> "foundation-core.commuting-squares-of-identifications" [arrowhead=none color="#28453010"] - "foundation.constant-type-families" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] - "foundation.constant-type-families" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.continuations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07068093650719452 shape=circle style=filled width=0.07068093650719452] - "foundation.continuations" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.type-arithmetic-unit-type" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "orthogonal-factorization-systems.extensions-maps" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "orthogonal-factorization-systems.types-local-at-maps" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.universal-property-empty-type" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "orthogonal-factorization-systems.modal-operators" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.evaluation-functions" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "orthogonal-factorization-systems.uniquely-eliminating-modalities" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.type-arithmetic-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.universal-property-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.continuations" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05943383002455521 shape=circle style=filled width=0.05943383002455521] - "foundation.contractible-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.contractible-maps" -> "foundation.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.contractible-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07244382412249044 shape=circle style=filled width=0.07244382412249044] - "foundation.contractible-types" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.constant-maps" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.contractible-types" -> "foundation.diagonal-maps-of-types" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] - "foundation.copartial-elements" -> "synthetic-homotopy-theory.joins-of-types" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" -> "foundation.partial-elements" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" -> "foundation.negation" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" -> "orthogonal-factorization-systems.closed-modalities" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.copartial-elements" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.copartial-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0690558701659274 shape=circle style=filled width=0.0690558701659274] - "foundation.copartial-functions" -> "foundation.partial-functions" [arrowhead=none color="#28453010"] - "foundation.copartial-functions" -> "foundation.copartial-elements" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.11287958111098491 shape=circle style=filled width=0.11287958111098491] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.equivalence-extensionality" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions-subuniverse" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] - 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color="#28453010"] - "foundation.coproduct-decompositions" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coproduct-decompositions" -> "foundation.type-arithmetic-empty-type" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08021208221262416 shape=circle style=filled width=0.08021208221262416] - "foundation.coproducts-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation.equality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.coproducts-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.coslice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.052921383526080924 shape=circle style=filled width=0.052921383526080924] - "foundation.coslice" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.coslice" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.coslice" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.coslice" -> "foundation.commuting-triangles-of-homotopies" [arrowhead=none color="#28453010"] - "foundation.cospan-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.cospan-diagrams" -> "foundation.cospans" [arrowhead=none 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"foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-function-types" -> "foundation.irrefutable-equality" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-function-types" -> "foundation.decidable-propositions" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-function-types" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-function-types" -> "foundation.universal-property-maybe" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-function-types" -> "logic.propositionally-decidable-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] - "foundation.decidable-dependent-pair-types" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.type-arithmetic-unit-type" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.uniformly-decidable-type-families" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.double-negation-dense-equality" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.type-arithmetic-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.maybe" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation.irrefutable-equality" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.decidable-dependent-pair-types" -> "logic.propositionally-decidable-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.12806379823024644 shape=circle style=filled width=0.12806379823024644] - "foundation.decidable-embeddings" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.cartesian-morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.retracts-of-maps" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.decidable-propositions" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.decidable-maps" [arrowhead=none color="#28453010"] - "foundation.decidable-embeddings" -> "foundation.propositional-maps" [arrowhead=none color="#28453010"] 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shape=circle style=filled width=0.05] - "foundation.discrete-binary-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.discrete-binary-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.discrete-binary-relations" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.discrete-reflexive-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.discrete-reflexive-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.discrete-reflexive-relations" -> "foundation.reflexive-relations" [arrowhead=none color="#28453010"] - "foundation.discrete-reflexive-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.discrete-reflexive-relations" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] - 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"foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.path-split-maps" -> "foundation-core.path-split-maps" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] - "foundation.path-split-type-families" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.dependent-identifications" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.path-split-type-families" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0816153154380072 shape=circle style=filled width=0.0816153154380072] - "foundation.perfect-images" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.iterated-dependent-product-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.empty-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.double-negation" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.decidable-types" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.negation" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.negated-equality" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.law-of-excluded-middle" [arrowhead=none color="#28453010"] - "foundation.perfect-images" -> "foundation.iterating-functions" 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"foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.pi-decompositions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.pi-decompositions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.pi-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.pi-decompositions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] - "foundation.pointed-torsorial-type-families" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.sorial-type-families" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.0-connected-types" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.pointed-torsorial-type-families" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] - "foundation.postcomposition-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] - "foundation.postcomposition-dependent-functions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.postcomposition-dependent-functions" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.postcomposition-dependent-functions" -> "foundation-core.postcomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.postcomposition-functions" [label="" color="#FFFFFF00" fillcolor="#284530" 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"foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.postcomposition-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.postcomposition-functions" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.postcomposition-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.postcomposition-functions" -> "foundation-core.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06776499241351715 shape=circle style=filled width=0.06776499241351715] - "foundation.postcomposition-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation.postcomposition-functions" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation.standard-pullbacks" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.postcomposition-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] - "foundation.powersets" 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"foundation.powersets" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.large-preorders" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "foundation.empty-types" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.posets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.dependent-products-large-preorders" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.suplattices" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.large-posets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.meet-semilattices" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.dependent-products-large-suplattices" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.bottom-elements-posets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.bottom-elements-large-posets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "foundation.large-locale-of-propositions" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.top-elements-posets" [arrowhead=none color="#28453010"] - "foundation.powersets" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06644904204903672 shape=circle style=filled width=0.06644904204903672] - "foundation.precomposition-dependent-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.precomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.truncated-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.precomposition-dependent-functions" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05985685194678195 shape=circle style=filled width=0.05985685194678195] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions-into-subuniverses" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.08253755166479786 shape=circle style=filled width=0.08253755166479786] - "foundation.precomposition-functions" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation.precomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.commuting-triangles-of-maps" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.precomposition-functions" -> "foundation.sections" [arrowhead=none color="#28453010"] - "foundation.precomposition-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.precomposition-type-families" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.precomposition-type-families" -> "foundation.transport-along-homotopies" [arrowhead=none color="#28453010"] - "foundation.precomposition-type-families" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.precomposition-type-families" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.preunivalence" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] - "foundation.preunivalence" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.preunivalence" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.preunivalence" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.06960177486788897 shape=circle style=filled width=0.06960177486788897] - "foundation.preunivalent-type-families" -> "foundation-core.univalence" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.faithful-maps" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.subuniverses" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.0-maps" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.preunivalence" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> "foundation.retractions" [arrowhead=none color="#28453010"] - "foundation.preunivalent-type-families" -> 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style=filled width=0.05] - "foundation.product-decompositions" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.products-binary-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.products-binary-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.products-binary-relations" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.products-binary-relations" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.products-equivalence-relations" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.products-equivalence-relations" -> "foundation.binary-relations" [arrowhead=none color="#28453010"] - "foundation.products-equivalence-relations" -> "foundation-core.equivalence-relations" [arrowhead=none 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[arrowhead=none color="#28453010"] - "foundation.sigma-decompositions" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.sigma-decompositions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.sigma-decompositions" -> "foundation.inhabited-types" [arrowhead=none color="#28453010"] - "foundation.singleton-induction" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] - "foundation.singleton-induction" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#28453010"] - "foundation.singleton-induction" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.singleton-induction" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.singleton-induction" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.singleton-subtypes" 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[arrowhead=none color="#28453010"] - "foundation.singleton-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.singleton-subtypes" -> "foundation.inhabited-subtypes" [arrowhead=none color="#28453010"] - "foundation.singleton-subtypes" -> "foundation.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.slice" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.09817510660004068 shape=circle style=filled width=0.09817510660004068] - "foundation.slice" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.homotopy-induction" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.families-of-equivalences" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.commuting-triangles-of-homotopies" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#28453010"] - "foundation.slice" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.slice" -> "trees.polynomial-endofunctors" [arrowhead=none color="#28453010"] - "foundation.small-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.small-maps" -> "foundation.retracts-of-maps" [arrowhead=none color="#28453010"] - "foundation.small-maps" -> "foundation.split-idempotent-maps" [arrowhead=none color="#28453010"] - "foundation.small-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.small-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.small-maps" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] - "foundation.small-maps" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] - "foundation.small-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.small-types" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.images" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.replacement" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation-core.embeddings" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.uniqueness-image" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.universal-property-image" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] - "foundation.small-types" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] - "foundation.small-universes" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.small-universes" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.small-universes" -> "foundation-core.small-types" [arrowhead=none color="#28453010"] - "foundation.sorial-type-families" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.sorial-type-families" -> "structured-types.pointed-types" [arrowhead=none color="#28453010"] - "foundation.span-diagrams-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.span-diagrams-families-of-types" -> "foundation.spans-families-of-types" [arrowhead=none color="#28453010"] - "foundation.span-diagrams" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05985685194678195 shape=circle style=filled width=0.05985685194678195] - "foundation.span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#28453010"] - "foundation.span-diagrams" -> "foundation.spans" [arrowhead=none color="#28453010"] - "foundation.spans-families-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.spans-of-spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] - "foundation.spans-of-spans" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.spans-of-spans" -> "foundation.spans" [arrowhead=none color="#28453010"] - "foundation.spans-of-spans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.spans" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.spans" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.17530461293723326 shape=circle style=filled width=0.17530461293723326] - "foundation.split-idempotent-maps" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.commuting-squares-of-homotopies" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.sets" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> 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"foundation.quasicoherently-idempotent-maps" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.inverse-sequential-diagrams" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.path-cosplit-maps" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.idempotent-maps" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.univalence" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation.weakly-constant-maps" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.split-idempotent-maps" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.split-surjective-maps" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.054564565808626536 shape=circle style=filled width=0.054564565808626536] - "foundation.split-surjective-maps" -> "foundation-core.retractions" [arrowhead=none color="#28453010"] - "foundation.split-surjective-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.split-surjective-maps" -> 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color="#28453010"] - "foundation.standard-apartness-relations" -> "foundation.law-of-excluded-middle" [arrowhead=none color="#28453010"] - "foundation.standard-apartness-relations" -> "foundation-core.negation" [arrowhead=none color="#28453010"] - "foundation.standard-apartness-relations" -> "foundation.apartness-relations" [arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.10046150864012858 shape=circle style=filled width=0.10046150864012858] - "foundation.standard-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - 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[arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" -> "foundation-core.diagonal-maps-cartesian-products-of-types" [arrowhead=none color="#28453010"] - "foundation.standard-pullbacks" -> "foundation-core.universal-property-pullbacks" [arrowhead=none color="#28453010"] - "foundation.standard-ternary-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.standard-ternary-pullbacks" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.standard-ternary-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] - "foundation.standard-ternary-pullbacks" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#28453010"] - "foundation.standard-ternary-pullbacks" -> "foundation.structure-identity-principle" [arrowhead=none color="#28453010"] - "foundation.standard-ternary-pullbacks" -> 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"foundation.universal-property-fiber-products" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-fiber-products" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-fiber-products" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-fiber-products" -> "foundation-core.equality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-fiber-products" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-systems" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05220133115091674 shape=circle style=filled width=0.05220133115091674] - "foundation.universal-property-identity-systems" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - 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"foundation.embeddings" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation.full-subtypes" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation.dependent-universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> "foundation.preunivalence" [arrowhead=none color="#28453010"] - "foundation.universal-property-identity-types" -> 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-> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.sections" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.propositional-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation.images" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.subtypes" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.injective-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-image" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.universal-property-maybe" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05 shape=circle style=filled width=0.05] - "foundation.universal-property-maybe" -> "foundation-core.coproduct-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-maybe" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.universal-property-maybe" -> "foundation.maybe" [arrowhead=none color="#28453010"] - "foundation.universal-property-maybe" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation-into-sets" [label="" color="#FFFFFF00" 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color="#FFFFFF00" fillcolor="#284530" height=0.09596572138218783 shape=circle style=filled width=0.09596572138218783] - "foundation.universal-property-propositional-truncation" -> "foundation.universal-property-equivalences" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.precomposition-dependent-functions" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation.precomposition-functions-into-subuniverses" [arrowhead=none color="#28453010"] - "foundation.universal-property-propositional-truncation" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.universal-property-pullbacks" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.07139131552728642 shape=circle style=filled width=0.07139131552728642] - "foundation.universal-property-pullbacks" -> "foundation.cones-over-cospan-diagrams" [arrowhead=none color="#28453010"] - "foundation.universal-property-pullbacks" -> "foundation-core.contractible-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-pullbacks" -> "foundation-core.pullbacks" [arrowhead=none color="#28453010"] - "foundation.universal-property-pullbacks" -> "foundation.subtype-identity-principle" [arrowhead=none color="#28453010"] - "foundation.universal-property-pullbacks" -> 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"foundation.universal-property-set-quotients" -> "foundation.propositional-extensionality" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.epimorphisms-with-respect-to-sets" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.equivalence-classes" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.existential-quantification" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.locally-small-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.injective-maps" [arrowhead=none color="#28453010"] - 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[arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.images" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation.surjective-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-quotients" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0760129244023573 shape=circle style=filled width=0.0760129244023573] - "foundation.universal-property-set-truncation" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#28453010"] - 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"foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-truncation" -> "foundation.mere-equality" [arrowhead=none color="#28453010"] - "foundation.universal-property-set-truncation" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.05195909628863885 shape=circle style=filled width=0.05195909628863885] - "foundation.universal-property-truncation" -> "foundation-core.contractible-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.truncation-levels" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.truncated-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.functoriality-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation.contractible-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation.type-arithmetic-dependent-function-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation.universal-property-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.type-theoretic-principle-of-choice" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#28453010"] - "foundation.universal-property-truncation" -> "foundation.surjective-maps" 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"foundation-core.homotopies" [arrowhead=none color="#28453010"] - "foundation.universal-property-unit-type" -> "foundation-core.precomposition-functions" [arrowhead=none color="#28453010"] - "foundation.universal-property-unit-type" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#28453010"] - "foundation.universal-quantification" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] - "foundation.universal-quantification" -> "foundation.evaluation-functions" [arrowhead=none color="#28453010"] - "foundation.universal-quantification" -> "foundation.logical-equivalences" [arrowhead=none color="#28453010"] - "foundation.universal-quantification" -> "foundation-core.propositions" [arrowhead=none color="#28453010"] - "foundation.unordered-pairs-of-types" [label="" color="#FFFFFF00" fillcolor="#284530" height=0.052682459581144495 shape=circle style=filled width=0.052682459581144495] - 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color="#96387210"] - "group-theory.commutator-subgroups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.commutator-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.commutators-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.060276905184077155 shape=circle style=filled width=0.060276905184077155] - "group-theory.commutators-of-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.commutators-of-elements-groups" -> "group-theory.commuting-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.commutators-of-elements-groups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.commutators-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.commuting-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05814630195131898 shape=circle style=filled width=0.05814630195131898] - "group-theory.commuting-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.commuting-elements-groups" -> "group-theory.commuting-elements-monoids" [arrowhead=none color="#96387210"] - "group-theory.commuting-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.054564565808626536 shape=circle style=filled width=0.054564565808626536] - "group-theory.commuting-elements-monoids" -> "group-theory.commuting-elements-semigroups" [arrowhead=none color="#96387210"] - "group-theory.commuting-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.commuting-elements-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] - "group-theory.commuting-elements-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - 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height=0.06373568211054055 shape=circle style=filled width=0.06373568211054055] - "group-theory.cyclic-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.cyclic-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.cyclic-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.cyclic-groups" -> "foundation.inhabited-subtypes" [arrowhead=none color="#96387210"] - "group-theory.cyclic-groups" -> "group-theory.generating-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10560411338421884 shape=circle style=filled width=0.10560411338421884] - "group-theory.decidable-subgroups" -> "foundation.decidable-subtypes" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.decidable-subgroups" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.dependent-products-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-abelian-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-abelian-groups" -> "group-theory.dependent-products-groups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.dependent-products-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-commutative-monoids" -> "group-theory.dependent-products-monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.050978647882712 shape=circle style=filled width=0.050978647882712] - "group-theory.dependent-products-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-groups" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.dependent-products-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-monoids" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.dependent-products-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.dependent-products-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-group-construction" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] - "group-theory.dihedral-group-construction" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-group-construction" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-group-construction" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-group-construction" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.dihedral-group-construction" -> "foundation.equality-coproduct-types" [arrowhead=none color="#96387210"] - "group-theory.dihedral-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.dihedral-groups" -> "elementary-number-theory.standard-cyclic-groups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.dihedral-groups" -> "group-theory.dihedral-group-construction" [arrowhead=none color="#96387210"] - "group-theory.e8-lattice" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.e8-lattice" -> "foundation.equality-coproduct-types" [arrowhead=none color="#96387210"] - "group-theory.e8-lattice" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] - "group-theory.e8-lattice" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.elements-of-finite-order-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "group-theory.orders-of-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "group-theory.subgroups-generated-by-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "elementary-number-theory.nonzero-integers" [arrowhead=none color="#96387210"] - "group-theory.elements-of-finite-order-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] - "group-theory.embeddings-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.embeddings-abelian-groups" -> "group-theory.embeddings-groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-abelian-groups" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-abelian-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.embeddings-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.embeddings-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.embeddings-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] - "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.integer-multiples-of-elements-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "group-theory.addition-homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "elementary-number-theory.ring-of-integers" [arrowhead=none color="#96387210"] - "group-theory.endomorphism-rings-abelian-groups" -> "ring-theory.rings" [arrowhead=none color="#96387210"] - "group-theory.epimorphisms-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.052682459581144495 shape=circle style=filled width=0.052682459581144495] - "group-theory.epimorphisms-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.epimorphisms-groups" -> "category-theory.epimorphisms-in-large-precategories" [arrowhead=none color="#96387210"] - "group-theory.epimorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.epimorphisms-groups" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] - "group-theory.epimorphisms-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] - "group-theory.equivalences-concrete-group-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "group-theory.homomorphisms-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "foundation.1-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-group-actions" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.equivalences-concrete-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-concrete-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10208095535698015 shape=circle style=filled width=0.10208095535698015] - "group-theory.equivalences-group-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.structure-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "group-theory.homomorphisms-group-actions" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "group-theory.symmetric-groups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-group-actions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] - "group-theory.equivalences-semigroups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" -> "foundation.structure-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.equivalences-semigroups" -> "foundation.univalence" [arrowhead=none color="#96387210"] - "group-theory.exponents-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.exponents-abelian-groups" -> "group-theory.exponents-groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-abelian-groups" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-abelian-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.exponents-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" -> "group-theory.free-groups-with-one-generator" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" -> "group-theory.intersections-subgroups-groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" -> "group-theory.kernels-homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.exponents-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] - "group-theory.free-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] - "group-theory.free-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.free-concrete-group-actions" -> "higher-group-theory.free-higher-group-actions" [arrowhead=none color="#96387210"] - "group-theory.free-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] - "group-theory.free-groups-with-one-generator" -> "structured-types.initial-pointed-type-equipped-with-automorphism" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "foundation.contractible-maps" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.free-groups-with-one-generator" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.0647177997777583 shape=circle style=filled width=0.0647177997777583] - "group-theory.full-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" -> "foundation.full-subtypes" [arrowhead=none color="#96387210"] - "group-theory.full-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06606824211104302 shape=circle style=filled width=0.06606824211104302] - "group-theory.full-subsemigroups" -> "group-theory.equivalences-semigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "group-theory.subsets-semigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "group-theory.isomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.full-subsemigroups" -> "foundation.full-subtypes" [arrowhead=none color="#96387210"] - "group-theory.function-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.function-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.function-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.function-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.function-abelian-groups" -> "group-theory.dependent-products-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.function-abelian-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.function-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.function-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.function-commutative-monoids" -> "group-theory.dependent-products-commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.function-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.function-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.function-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.function-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.function-groups" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.function-groups" -> "group-theory.dependent-products-groups" [arrowhead=none color="#96387210"] - "group-theory.function-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.function-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.function-monoids" -> "group-theory.dependent-products-monoids" [arrowhead=none color="#96387210"] - "group-theory.function-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.function-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.function-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.function-semigroups" -> "group-theory.dependent-products-semigroups" [arrowhead=none color="#96387210"] - 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[arrowhead=none color="#96387210"] - "group-theory.functoriality-quotient-groups" -> "group-theory.homomorphisms-groups-equipped-with-normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.functoriality-quotient-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] - "group-theory.furstenberg-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.generating-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13137046916338763 shape=circle style=filled width=0.13137046916338763] - "group-theory.generating-elements-groups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.generating-elements-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] - "group-theory.generating-elements-groups" -> "ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - 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shape=circle style=filled width=0.09424124867625935] - "group-theory.homomorphisms-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-groups" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-groups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] - "group-theory.homomorphisms-monoids" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07814071540843244 shape=circle style=filled width=0.07814071540843244] - "group-theory.homomorphisms-semigroups" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-semigroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.homomorphisms-semigroups" -> "foundation.homotopy-induction" [arrowhead=none color="#96387210"] - 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-> "group-theory.automorphism-groups" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.09069398819863565 shape=circle style=filled width=0.09069398819863565] - "group-theory.images-of-group-homomorphisms" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.images-of-group-homomorphisms" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - 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"group-theory.monoid-actions" -> "foundation.endomorphisms" [arrowhead=none color="#96387210"] - "group-theory.monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.067391628732453 shape=circle style=filled width=0.067391628732453] - "group-theory.monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.monoids" -> "structured-types.h-spaces" [arrowhead=none color="#96387210"] - "group-theory.monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#96387210"] - "group-theory.monoids" -> "foundation.unital-binary-operations" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.monomorphisms-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-concrete-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.monomorphisms-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-groups" -> "category-theory.monomorphisms-in-large-precategories" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-groups" -> "group-theory.precategory-of-groups" [arrowhead=none color="#96387210"] - "group-theory.monomorphisms-groups" -> "group-theory.isomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.multiples-of-elements-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] - "group-theory.multiples-of-elements-abelian-groups" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.multiples-of-elements-abelian-groups" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.multiples-of-elements-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.multiples-of-elements-abelian-groups" -> "group-theory.powers-of-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] - "group-theory.nontrivial-groups" -> "group-theory.trivial-groups" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.propositional-extensionality" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.injective-maps" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.disjunction" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.negation" [arrowhead=none color="#96387210"] - "group-theory.nontrivial-groups" -> "foundation.negated-equality" [arrowhead=none color="#96387210"] - 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-> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.normal-closures-subgroups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.normal-closures-subgroups" -> "group-theory.subgroups-generated-by-subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.normal-closures-subgroups" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#96387210"] - "group-theory.normal-closures-subgroups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.normal-closures-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.normal-cores-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] - "group-theory.normal-cores-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.normal-cores-subgroups" -> 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style=filled width=0.13374970032900724] - "group-theory.normal-subgroups" -> "group-theory.congruence-relations-groups" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.normal-subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - 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color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.mere-equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] - "group-theory.orbit-stabilizer-theorem-concrete-groups" -> "group-theory.stabilizer-groups-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.orbits-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.orbits-concrete-group-actions" -> 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color="#96387210"] - "group-theory.perfect-cores" -> "group-theory.perfect-subgroups" [arrowhead=none color="#96387210"] - "group-theory.perfect-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.perfect-groups" -> "group-theory.full-subgroups" [arrowhead=none color="#96387210"] - "group-theory.perfect-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.perfect-groups" -> "group-theory.commutator-subgroups" [arrowhead=none color="#96387210"] - "group-theory.perfect-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.perfect-subgroups" -> "group-theory.perfect-groups" [arrowhead=none color="#96387210"] - "group-theory.perfect-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.perfect-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - 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height=0.06960177486788897 shape=circle style=filled width=0.06960177486788897] - "group-theory.powers-of-elements-groups" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-groups" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-groups" -> "group-theory.commuting-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-groups" -> "group-theory.powers-of-elements-monoids" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.0911103361631442 shape=circle style=filled width=0.0911103361631442] - "group-theory.powers-of-elements-monoids" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-monoids" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.powers-of-elements-monoids" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-commutative-monoids" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-commutative-monoids" -> "group-theory.precategory-of-monoids" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-commutative-monoids" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-commutative-monoids" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-concrete-groups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-group-actions" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-group-actions" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-group-actions" -> "group-theory.homomorphisms-group-actions" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-groups" -> "group-theory.precategory-of-semigroups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-groups" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-groups" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-groups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-monoids" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" -> "group-theory.precategory-of-semigroups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-monoids" -> "category-theory.large-subprecategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06923831664020327 shape=circle style=filled width=0.06923831664020327] - "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-orbits-monoid-actions" -> "group-theory.monoid-actions" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.precategory-of-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-semigroups" -> "category-theory.large-precategories" [arrowhead=none color="#96387210"] - "group-theory.precategory-of-semigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.principal-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.principal-group-actions" -> "foundation.equivalence-extensionality" [arrowhead=none color="#96387210"] - "group-theory.principal-group-actions" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.principal-group-actions" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] - "group-theory.principal-torsors-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.principal-torsors-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.principal-torsors-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.products-of-elements-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.products-of-elements-monoids" -> "lists.concatenation-lists" [arrowhead=none color="#96387210"] - "group-theory.products-of-elements-monoids" -> "lists.lists" [arrowhead=none color="#96387210"] - "group-theory.products-of-elements-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07683827893814787 shape=circle style=filled width=0.07683827893814787] - "group-theory.pullbacks-subgroups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.pullbacks-subsemigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subgroups" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06353743689589825 shape=circle style=filled width=0.06353743689589825] - "group-theory.pullbacks-subsemigroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "group-theory.subsets-semigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#96387210"] - "group-theory.pullbacks-subsemigroups" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.06887294038719267 shape=circle style=filled width=0.06887294038719267] - "group-theory.quotient-groups-concrete-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups-concrete-groups" -> "foundation.0-images-of-maps" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups-concrete-groups" -> "foundation.1-types" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups-concrete-groups" -> "group-theory.mere-equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] - 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color="#96387210"] - "group-theory.quotient-groups-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13440833808089672 shape=circle style=filled width=0.13440833808089672] - "group-theory.quotient-groups" -> "foundation.commuting-triangles-of-maps" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.set-quotients" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "group-theory.nullifying-group-homomorphisms" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.contractible-types" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.contractible-maps" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.surjective-maps" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.quotient-groups" -> 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[arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "group-theory.nullifying-group-homomorphisms" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "group-theory.quotient-groups" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.universal-property-set-quotients" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.reflecting-maps-equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.surjective-maps" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.effective-maps-equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.binary-functoriality-set-quotients" [arrowhead=none color="#96387210"] - "group-theory.quotients-abelian-groups" -> "foundation.functoriality-set-quotients" [arrowhead=none color="#96387210"] - "group-theory.rational-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] - "group-theory.rational-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.rational-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.rational-commutative-monoids" -> "group-theory.powers-of-elements-commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.representations-monoids-precategories" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.059007775570652274 shape=circle style=filled width=0.059007775570652274] - "group-theory.representations-monoids-precategories" -> "category-theory.precategories" [arrowhead=none color="#96387210"] - 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color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "group-theory.congruence-relations-commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-commutative-monoids" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07484213832213174 shape=circle style=filled width=0.07484213832213174] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.torsorial-type-families" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#96387210"] - "group-theory.saturated-congruence-relations-monoids" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] - "group-theory.semigroups" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#96387210"] - "group-theory.sheargroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.shriek-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.shriek-concrete-group-actions" -> "foundation.set-truncations" [arrowhead=none color="#96387210"] - "group-theory.shriek-concrete-group-actions" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.shriek-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.shriek-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.stabilizer-groups-concrete-group-actions" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "group-theory.subgroups-concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "foundation.mere-equality" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "group-theory.transitive-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups-concrete-group-actions" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.stabilizer-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.stabilizer-groups" -> "group-theory.group-actions" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13213648422208604 shape=circle style=filled width=0.13213648422208604] - "group-theory.subgroups-abelian-groups" -> "group-theory.congruence-relations-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "order-theory.large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "order-theory.posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.subsets-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.congruence-relations-abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "foundation.large-binary-relations" [arrowhead=none color="#96387210"] - "group-theory.subgroups-abelian-groups" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07942179611987281 shape=circle style=filled width=0.07942179611987281] - "group-theory.subgroups-concrete-groups" -> "structured-types.pointed-maps" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.homomorphisms-concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "foundation.structure-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "foundation.faithful-maps" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "foundation.existential-quantification" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.transitive-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "foundation.0-maps" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "structured-types.pointed-types" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "synthetic-homotopy-theory.functoriality-loop-spaces" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.orbits-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.equivalences-concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "foundation.0-connected-types" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-concrete-groups" -> "group-theory.concrete-group-actions" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.10071234925192582 shape=circle style=filled width=0.10071234925192582] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.subgroups-generated-by-subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.trivial-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "foundation.images-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.images-of-group-homomorphisms" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "group-theory.free-groups-with-one-generator" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "foundation.singleton-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-elements-groups" -> "elementary-number-theory.group-of-integers" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.subgroups-generated-by-subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "foundation.universal-property-image" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "foundation.images" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "foundation.images-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.trivial-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.images-of-group-homomorphisms" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-families-of-elements-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.12487167508965843 shape=circle style=filled width=0.12487167508965843] - "group-theory.subgroups-generated-by-subsets-groups" -> "lists.concatenation-lists" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.conjugation" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.normal-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "lists.lists" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.commuting-squares-of-galois-connections-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.singleton-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.fibers-of-maps" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.pullbacks-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.pullbacks-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.trivial-subgroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "foundation.images-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.images-of-group-homomorphisms" [arrowhead=none color="#96387210"] - "group-theory.subgroups-generated-by-subsets-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.13627262043998845 shape=circle style=filled width=0.13627262043998845] - "group-theory.subgroups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.logical-equivalences" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.injective-maps" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.disjunction" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.integer-powers-of-elements-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "elementary-number-theory.integers" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.large-binary-relations" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.embeddings" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.binary-relations" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.subsemigroups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subgroups" -> "foundation.equivalence-relations" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07450424883882695 shape=circle style=filled width=0.07450424883882695] - "group-theory.submonoids-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" -> "group-theory.subsets-commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" -> "group-theory.submonoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids-commutative-monoids" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.07279127850973344 shape=circle style=filled width=0.07279127850973344] - "group-theory.submonoids" -> "group-theory.subsets-monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.submonoids" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.submonoids" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#96387210"] - "group-theory.submonoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.08743614755394276 shape=circle style=filled width=0.08743614755394276] - "group-theory.subsemigroups" -> "group-theory.subsets-semigroups" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.preorders" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.large-preorders" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.posets" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#96387210"] - "group-theory.subsemigroups" -> "foundation.large-binary-relations" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.subsets-abelian-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" -> "group-theory.abelian-groups" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" -> "group-theory.subsets-groups" [arrowhead=none color="#96387210"] - "group-theory.subsets-abelian-groups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - "group-theory.subsets-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05147120664547112 shape=circle style=filled width=0.05147120664547112] - "group-theory.subsets-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.subsets-commutative-monoids" -> "group-theory.subsets-monoids" [arrowhead=none color="#96387210"] - "group-theory.subsets-groups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.subsets-groups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subsets-groups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subsets-groups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.subsets-groups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] - "group-theory.subsets-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.subsets-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "group-theory.subsets-semigroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.053631769453388635 shape=circle style=filled width=0.053631769453388635] - "group-theory.subsets-semigroups" -> "order-theory.large-posets" [arrowhead=none color="#96387210"] - "group-theory.subsets-semigroups" -> "group-theory.semigroups" [arrowhead=none color="#96387210"] - "group-theory.subsets-semigroups" -> "order-theory.large-locales" [arrowhead=none color="#96387210"] - "group-theory.subsets-semigroups" -> "foundation.large-locale-of-subtypes" [arrowhead=none color="#96387210"] - "group-theory.subsets-semigroups" -> "foundation.powersets" [arrowhead=none color="#96387210"] - 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"group-theory.trivial-groups" -> "group-theory.full-subgroups" [arrowhead=none color="#96387210"] - "group-theory.trivial-subgroups" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.trivial-subgroups" -> "group-theory.groups" [arrowhead=none color="#96387210"] - "group-theory.trivial-subgroups" -> "group-theory.subgroups" [arrowhead=none color="#96387210"] - "group-theory.unordered-tuples-in-commutative-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.unordered-tuples-in-commutative-monoids" -> "group-theory.commutative-monoids" [arrowhead=none color="#96387210"] - "group-theory.unordered-tuples-in-commutative-monoids" -> "foundation.unordered-tuples" [arrowhead=none color="#96387210"] - "group-theory.wild-representations-monoids" [label="" color="#FFFFFF00" fillcolor="#963872" height=0.05 shape=circle style=filled width=0.05] - "group-theory.wild-representations-monoids" -> "foundation.endomorphisms" [arrowhead=none color="#96387210"] - "group-theory.wild-representations-monoids" -> "structured-types.morphisms-wild-monoids" [arrowhead=none color="#96387210"] - "group-theory.wild-representations-monoids" -> "group-theory.monoids" [arrowhead=none color="#96387210"] - "higher-group-theory.abelian-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.abelian-higher-groups" -> "foundation.small-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "structured-types.small-pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "synthetic-homotopy-theory.connective-spectra" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "higher-group-theory.small-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.abelian-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] - "higher-group-theory.automorphism-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.1-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.connected-components" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.contractible-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "group-theory.equivalences-concrete-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "group-theory.concrete-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.automorphism-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] - "higher-group-theory.cartesian-products-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "structured-types.pointed-cartesian-product-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "foundation.mere-equality" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cartesian-products-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.conjugation" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.conjugation" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.conjugation" -> "synthetic-homotopy-theory.conjugation-loops" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.conjugation" -> "higher-group-theory.homomorphisms-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.conjugation" -> "structured-types.conjugation-pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cyclic-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.cyclic-higher-groups" -> "foundation.embeddings" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cyclic-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cyclic-higher-groups" -> "higher-group-theory.homomorphisms-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.cyclic-higher-groups" -> "foundation.existential-quantification" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.deloopable-groups" -> "higher-group-theory.deloopable-h-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-groups" -> "group-theory.groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-h-spaces" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.deloopable-h-spaces" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-h-spaces" -> "structured-types.equivalences-h-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.07568026230535431 shape=circle style=filled width=0.07568026230535431] - "higher-group-theory.deloopable-types" -> "foundation.small-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "structured-types.small-pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "higher-group-theory.equivalences-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "higher-group-theory.small-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.deloopable-types" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05922118594381655 shape=circle style=filled width=0.05922118594381655] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "foundation.truncation-levels" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "group-theory.groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "structured-types.equivalences-h-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "group-theory.abelian-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "synthetic-homotopy-theory.iterated-loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "foundation.connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.eilenberg-mac-lane-spaces" -> "foundation.truncated-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05433286809186783 shape=circle style=filled width=0.05433286809186783] - "higher-group-theory.equivalences-higher-groups" -> "foundation.torsorial-type-families" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "synthetic-homotopy-theory.functoriality-loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "foundation.subtype-identity-principle" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "higher-group-theory.homomorphisms-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "structured-types.pointed-isomorphisms" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.equivalences-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.fixed-points-higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.fixed-points-higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.fixed-points-higher-group-actions" -> "higher-group-theory.higher-group-actions" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.0629389547650211 shape=circle style=filled width=0.0629389547650211] - "higher-group-theory.free-higher-group-actions" -> "foundation.truncation-levels" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "higher-group-theory.orbits-higher-group-actions" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "foundation.embeddings" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "foundation.regensburg-extension-fundamental-theorem-of-identity-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "foundation.propositional-maps" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.free-higher-group-actions" -> "higher-group-theory.higher-group-actions" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.06131444962281207 shape=circle style=filled width=0.06131444962281207] - "higher-group-theory.higher-groups" -> "foundation.images" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "structured-types.h-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "foundation.full-subtypes" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "foundation.mere-equality" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.homomorphisms-higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-group-actions" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-group-actions" -> "higher-group-theory.higher-group-actions" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.057710742994894 shape=circle style=filled width=0.057710742994894] - "higher-group-theory.homomorphisms-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-groups" -> "structured-types.pointed-maps" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-groups" -> "synthetic-homotopy-theory.functoriality-loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.homomorphisms-higher-groups" -> "structured-types.pointed-homotopies" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.integers-higher-group" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.integers-higher-group" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.integers-higher-group" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.integers-higher-group" -> "synthetic-homotopy-theory.circle" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.07244382412249044 shape=circle style=filled width=0.07244382412249044] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "higher-group-theory.cartesian-products-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "foundation.iterated-cartesian-product-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "foundation.contractible-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "higher-group-theory.trivial-higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "synthetic-homotopy-theory.loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "foundation.mere-equality" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-cartesian-products-higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-deloopings-of-pointed-types" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.iterated-deloopings-of-pointed-types" -> "foundation.truncation-levels" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-deloopings-of-pointed-types" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-deloopings-of-pointed-types" -> "synthetic-homotopy-theory.iterated-loop-spaces" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-deloopings-of-pointed-types" -> "foundation.connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.iterated-deloopings-of-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.orbits-higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.orbits-higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.orbits-higher-group-actions" -> "higher-group-theory.higher-group-actions" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.08815461606208143 shape=circle style=filled width=0.08815461606208143] - "higher-group-theory.small-higher-groups" -> "foundation.small-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "structured-types.small-pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "structured-types.pointed-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "foundation.replacement" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "foundation.locally-small-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.small-higher-groups" -> 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fillcolor="#E79FEE" height=0.05 shape=circle style=filled width=0.05] - "higher-group-theory.symmetric-higher-groups" -> "foundation.mere-equivalences" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.symmetric-higher-groups" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.symmetric-higher-groups" -> "foundation.0-connected-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.symmetric-higher-groups" -> "foundation.connected-components-universes" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.symmetric-higher-groups" -> "structured-types.pointed-types" [arrowhead=none color="#E79FEE10"] - "higher-group-theory.transitive-higher-group-actions" [label="" color="#FFFFFF00" fillcolor="#E79FEE" height=0.08146059432173196 shape=circle style=filled width=0.08146059432173196] - "higher-group-theory.transitive-higher-group-actions" -> "higher-group-theory.higher-groups" [arrowhead=none color="#E79FEE10"] - 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shape=circle style=filled width=0.11498345220469042] - "logic.double-negation-dense-maps" -> "logic.irrefutable-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "logic.double-negation-stable-embeddings" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.contractible-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.truncation-levels" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.subtype-identity-principle" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.connected-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.structure-identity-principle" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.retracts-of-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.sections" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.split-surjective-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.double-negation" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.homotopies" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.homotopy-induction" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.surjective-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.univalence" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-maps" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-subtypes" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.060276905184077155 shape=circle style=filled width=0.060276905184077155] - "logic.double-negation-dense-subtypes" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-subtypes" -> "foundation.double-negation" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-dense-subtypes" -> 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"logic.double-negation-eliminating-maps" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-eliminating-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-eliminating-maps" -> "logic.double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-eliminating-maps" -> "foundation.decidable-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-eliminating-maps" -> "foundation.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.08656611449234101 shape=circle style=filled width=0.08656611449234101] - "logic.double-negation-elimination" -> "foundation-core.contractible-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.double-negation-dense-equality" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.double-negation" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.evaluation-functions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.retracts-of-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.irrefutable-equality" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.mere-equality" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-elimination" -> "foundation.hilberts-epsilon-operators" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.136642424703178 shape=circle style=filled width=0.136642424703178] - "logic.double-negation-stable-embeddings" -> "foundation.cartesian-morphisms-arrows" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.universal-property-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.fibers-of-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.embeddings" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.retracts-of-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "logic.double-negation-eliminating-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.homotopies" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.decidable-embeddings" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.homotopy-induction" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "logic.double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation-core.injective-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.double-negation-stable-propositions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-embeddings" -> "foundation.propositional-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.09234811820996562 shape=circle style=filled width=0.09234811820996562] - "logic.double-negation-stable-subtypes" -> "foundation-core.transport-along-identifications" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "logic.double-negation-stable-embeddings" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.truncation-levels" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.truncated-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.1-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.embeddings" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.double-negation-stable-propositions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "logic.double-negation-eliminating-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "logic.double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.injective-maps" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.type-theoretic-principle-of-choice" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.structured-type-duality" [arrowhead=none color="#A9CFCE10"] - "logic.double-negation-stable-subtypes" -> "foundation.propositional-maps" [arrowhead=none color="#A9CFCE10"] - "logic.functoriality-existential-quantification" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.05814630195131898 shape=circle style=filled width=0.05814630195131898] - "logic.functoriality-existential-quantification" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.functoriality-existential-quantification" -> "foundation.existential-quantification" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.06644904204903672 shape=circle style=filled width=0.06644904204903672] - "logic.irrefutable-types" -> "foundation.double-negation" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "logic.double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.contractible-types" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.subuniverses" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.irrefutable-types" -> "foundation.inhabited-types" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.05 shape=circle style=filled width=0.05] - "logic.markovian-types" -> "foundation.decidable-subtypes" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" -> "foundation.existential-quantification" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" -> "foundation.booleans" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" -> "foundation.universal-quantification" [arrowhead=none color="#A9CFCE10"] - "logic.markovian-types" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.05 shape=circle style=filled width=0.05] - "logic.markovs-principle" -> "foundation.decidable-subtypes" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "logic.markovian-types" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.existential-quantification" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.booleans" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.universal-quantification" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation-core.sets" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.disjunction" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.markovs-principle" -> "foundation.inhabited-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.08314669315133152 shape=circle style=filled width=0.08314669315133152] - "logic.propositional-double-negation-elimination" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.double-negation-dense-equality" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.double-negation" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.retracts-of-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.irrefutable-equality" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "logic.double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.mere-equality" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "foundation.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositional-double-negation-elimination" -> "logic.propositionally-decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.0686895234426777 shape=circle style=filled width=0.0686895234426777] - "logic.propositionally-decidable-maps" -> "foundation.double-negation-dense-equality-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation-core.homotopies" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation-core.injective-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation.decidable-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation.decidable-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "logic.propositionally-decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-maps" -> "foundation-core.iterating-functions" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.09557052798858454 shape=circle style=filled width=0.09557052798858454] - "logic.propositionally-decidable-types" -> "foundation-core.decidable-propositions" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.logical-equivalences" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.decidable-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.functoriality-coproduct-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.negation" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.retracts-of-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation-core.propositions" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.empty-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-decidable-types" -> "foundation.coinhabited-pairs-of-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" [label="" color="#FFFFFF00" fillcolor="#A9CFCE" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] - "logic.propositionally-double-negation-eliminating-maps" -> "logic.double-negation-eliminating-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" -> "foundation-core.homotopies" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" -> "foundation-core.functoriality-dependent-pair-types" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" -> "logic.propositional-double-negation-elimination" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" -> "logic.propositionally-decidable-maps" [arrowhead=none color="#A9CFCE10"] - "logic.propositionally-double-negation-eliminating-maps" -> "foundation-core.fibers-of-maps" [arrowhead=none color="#A9CFCE10"] - "metric-spaces.approximations-located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.approximations-located-metric-spaces" -> "metric-spaces.approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "metric-spaces.located-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-located-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.07830199672637511 shape=circle style=filled width=0.07830199672637511] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.images-isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.images-short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "foundation.images-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.images-uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.approximations-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.11476380835140088 shape=circle style=filled width=0.11476380835140088] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.indexed-sums-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.equivalence-classes" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.set-quotients" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.elements-at-bounded-distance-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.contractible-maps" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.bounded-distance-decompositions-of-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "foundation.conjunction" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cartesian-products-metric-spaces" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-isometries" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.category-of-metric-spaces-and-isometries" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-isometries" -> "metric-spaces.precategory-of-metric-spaces-and-isometries" 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"metric-spaces.category-of-metric-spaces-and-short-functions" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "category-theory.categories" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] - "metric-spaces.category-of-metric-spaces-and-short-functions" -> "foundation.functoriality-dependent-pair-types" 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"foundation.constant-maps" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-approximations-metric-spaces" -> "metric-spaces.cauchy-approximations-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-approximations-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] - "metric-spaces.cauchy-approximations-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-approximations-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-approximations-pseudometric-spaces" -> "metric-spaces.short-functions-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "metric-spaces.cauchy-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-complete-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.12855540770864293 shape=circle style=filled width=0.12855540770864293] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.limits-of-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.archimedean-property-positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.nonzero-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.unit-fractions-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "foundation.binary-transport" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "metric-spaces.convergent-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.multiplicative-group-of-positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.cauchy-sequences-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.closed-subsets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-located-metric-spaces" -> "metric-spaces.located-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08435178051687288 shape=circle style=filled width=0.08435178051687288] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.closure-subsets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.intersections-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.discrete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.dependent-products-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.open-subsets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.dense-subsets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.disjunction" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "metric-spaces.dependent-products-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.complements-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.closed-subsets-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.055708601453115555 shape=circle style=filled width=0.055708601453115555] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.intersections-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.closure-subsets-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.compact-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.compact-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.compact-metric-spaces" -> "metric-spaces.totally-bounded-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.compact-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.compact-metric-spaces" -> "foundation.conjunction" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.06587701669662775 shape=circle style=filled width=0.06587701669662775] - "metric-spaces.complete-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "foundation.retractions" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.complete-metric-spaces" -> "foundation.sections" [arrowhead=none color="#923E8210"] - "metric-spaces.continuous-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.continuous-functions-metric-spaces" -> "metric-spaces.limits-of-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.continuous-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.continuous-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.continuous-functions-metric-spaces" -> 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"metric-spaces.convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.convergent-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] - "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.limits-of-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.convergent-sequences-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] - "metric-spaces.convergent-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.closure-subsets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.dense-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - 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color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.dependent-products-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - 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"metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.discrete-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.discrete-metric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.discrete-metric-spaces" -> "metric-spaces.locally-constant-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.discrete-metric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] - "metric-spaces.discrete-metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08146059432173196 shape=circle style=filled width=0.08146059432173196] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "order-theory.preorders" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.inequality-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.functoriality-propositional-truncation" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.negation" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.rational-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.elements-at-bounded-distance-metric-spaces" -> "real-numbers.minimum-upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08612780223548151 shape=circle style=filled width=0.08612780223548151] - "metric-spaces.equality-of-metric-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.equality-of-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.retractions" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "foundation.sections" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08021208221262416 shape=circle style=filled width=0.08021208221262416] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.functions-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.contractible-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "metric-spaces.isometries-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.univalence" [arrowhead=none color="#923E8210"] - "metric-spaces.equality-of-pseudometric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] - "metric-spaces.extensionality-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.0686895234426777 shape=circle style=filled width=0.0686895234426777] - "metric-spaces.extensionality-pseudometric-spaces" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] - "metric-spaces.extensionality-pseudometric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.extensionality-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.extensionality-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.extensionality-pseudometric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functions-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.functions-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.category-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.faithful-functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.category-of-sets" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.maps-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.conservative-functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.isomorphisms-of-sets" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-set-functions-isometry-metric-spaces" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.faithful-functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.split-essentially-surjective-functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.maps-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.conservative-functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-isometries" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.functors-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#923E8210"] - "metric-spaces.functor-category-short-isometry-metric-spaces" -> "metric-spaces.precategory-of-metric-spaces-and-short-functions" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-isometries-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.images-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.images-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-short-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-short-functions-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-short-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "foundation.images" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.images-uniformly-continuous-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09221140737526 shape=circle style=filled width=0.09221140737526] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.discrete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.similarity-of-elements-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.locally-constant-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.indexed-sums-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.interior-subsets-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.unions-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.raising-universe-levels" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.interior-subsets-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.isometries-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09983164971226559 shape=circle style=filled width=0.09983164971226559] - "metric-spaces.isometries-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - 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"metric-spaces.limits-of-sequences-metric-spaces" -> "elementary-number-theory.maximum-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.limits-of-sequences-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.limits-of-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.limits-of-sequences-metric-spaces" -> "foundation.inhabited-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.limits-of-sequences-metric-spaces" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.1026970198232252 shape=circle style=filled width=0.1026970198232252] - "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.elements-at-bounded-distance-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.lipschitz-functions-metric-spaces" -> 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color="#923E8210"] - "metric-spaces.locally-constant-functions-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.locally-constant-functions-metric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.067391628732453 shape=circle style=filled width=0.067391628732453] - "metric-spaces.located-metric-spaces" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> 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"real-numbers.dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "foundation.negation" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "foundation.functoriality-disjunction" [arrowhead=none color="#923E8210"] - "metric-spaces.located-metric-spaces" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09557052798858454 shape=circle style=filled width=0.09557052798858454] - "metric-spaces.metric-space-of-cauchy-approximations-complete-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" 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color="#923E8210"] - "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.metric-space-of-convergent-cauchy-approximations-metric-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#923E8210"] - "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.subspaces-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.convergent-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.metric-space-of-convergent-sequences-metric-spaces" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] - 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"metric-spaces.rational-approximations-of-zero" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "metric-spaces.rational-cauchy-approximations" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "foundation.retractions" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "elementary-number-theory.absolute-value-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "elementary-number-theory.distance-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "foundation.sections" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-approximations-of-zero" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] - "metric-spaces.rational-cauchy-approximations" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "real-numbers.metric-space-of-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.metric-space-of-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.complete-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "elementary-number-theory.absolute-value-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> "real-numbers.cauchy-completeness-dedekind-real-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-cauchy-approximations" -> 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[arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.negation" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.univalence" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.empty-types" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-neighborhood-relations" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.07862356685452848 shape=circle style=filled width=0.07862356685452848] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.metric-space-of-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.nonnegative-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.rational-cauchy-approximations" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.convergent-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.rational-approximations-of-zero" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.inequality-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.limits-of-sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "lists.sequences" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.limits-of-cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.nonzero-natural-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.unit-fractions-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.cauchy-approximations-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.absolute-value-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "metric-spaces.sequences-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.distance-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.rational-sequences-approximating-zero" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.reflexive-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.reflexive-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.reflexive-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.reflexive-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.07296438524291976 shape=circle style=filled width=0.07296438524291976] - "metric-spaces.saturated-rational-neighborhood-relations" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.propositional-extensionality" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "metric-spaces.poset-of-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.univalence" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.saturated-rational-neighborhood-relations" -> "foundation.torsorial-type-families" [arrowhead=none color="#923E8210"] - 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"metric-spaces.short-functions-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.09207449355456987 shape=circle style=filled width=0.09207449355456987] - "metric-spaces.short-functions-pseudometric-spaces" -> "metric-spaces.functions-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "foundation.existential-quantification" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "foundation.embeddings" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "lists.sequences" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "metric-spaces.poset-of-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "metric-spaces.isometries-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.short-functions-pseudometric-spaces" -> "metric-spaces.preimages-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08099465764396384 shape=circle style=filled width=0.08099465764396384] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.similarity-of-elements-pseudometric-spaces" -> "foundation.equivalence-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.07050222336024897 shape=circle style=filled width=0.07050222336024897] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.triangular-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "foundation.logical-equivalences" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "foundation.full-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.symmetric-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.saturated-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.extensionality-pseudometric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "foundation.empty-subtypes" [arrowhead=none color="#923E8210"] - "metric-spaces.subspaces-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.symmetric-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.symmetric-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.symmetric-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.symmetric-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.0668276721338242 shape=circle style=filled width=0.0668276721338242] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-short-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.equality-of-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.isometries-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-uniformly-continuous-functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.images-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.nets-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "foundation.inhabited-types" [arrowhead=none color="#923E8210"] - "metric-spaces.totally-bounded-metric-spaces" -> "metric-spaces.functions-metric-spaces" [arrowhead=none color="#923E8210"] - "metric-spaces.triangular-rational-neighborhood-relations" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.05 shape=circle style=filled width=0.05] - "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.reflexive-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.triangular-rational-neighborhood-relations" -> "foundation.binary-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.triangular-rational-neighborhood-relations" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#923E8210"] - "metric-spaces.triangular-rational-neighborhood-relations" -> "metric-spaces.monotonic-rational-neighborhood-relations" [arrowhead=none color="#923E8210"] - "metric-spaces.uniformly-continuous-functions-metric-spaces" [label="" color="#FFFFFF00" fillcolor="#923E82" height=0.08284268228643028 shape=circle style=filled 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color="#E45F8510"] - "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-dependent-pair-types" -> "modal-type-theory.flat-discrete-crisp-types" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-dependent-pair-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-dependent-pair-types" -> "foundation.sections" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-function-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.05660718525986409 shape=circle style=filled width=0.05660718525986409] - "modal-type-theory.crisp-function-types" -> "foundation.postcomposition-functions" [arrowhead=none color="#E45F8510"] - "modal-type-theory.crisp-function-types" -> 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-> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" [label="" color="#FFFFFF00" fillcolor="#E45F85" height=0.0911103361631442 shape=circle style=filled width=0.0911103361631442] - "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.action-on-homotopies-flat-modality" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.functoriality-flat-modality" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" -> "foundation.embeddings" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" -> "foundation.booleans" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.crisp-identity-types" [arrowhead=none color="#E45F8510"] - "modal-type-theory.flat-discrete-crisp-types" -> "modal-type-theory.flat-modality" [arrowhead=none color="#E45F8510"] - 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"order-theory.closure-operators-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-locales" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-locales" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07226947050238228 shape=circle style=filled width=0.07226947050238228] - "order-theory.closure-operators-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-posets" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-posets" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.closure-operators-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-galois-connections-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.054100178080045934 shape=circle style=filled width=0.054100178080045934] - "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-galois-connections-large-posets" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-order-preserving-maps-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#533A2210"] - "order-theory.commuting-squares-of-order-preserving-maps-large-posets" -> "order-theory.similarity-of-order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.coverings-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.coverings-locales" -> "order-theory.locales" [arrowhead=none color="#533A2210"] - "order-theory.decidable-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] - "order-theory.decidable-posets" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-posets" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] - "order-theory.decidable-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.decidable-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] - "order-theory.decidable-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subposets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.decidable-subposets" -> "foundation.decidable-subtypes" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subposets" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subposets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subposets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subpreorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.decidable-subpreorders" -> "foundation.decidable-subtypes" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subpreorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subpreorders" -> "order-theory.subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-subpreorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.1234491685859344 shape=circle style=filled width=0.1234491685859344] - "order-theory.decidable-total-orders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.decidable-posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.decidable-total-preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.greatest-lower-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.subposets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.join-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-orders" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] - "order-theory.decidable-total-preorders" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "order-theory.total-preorders" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] - "order-theory.decidable-total-preorders" -> "foundation.empty-types" [arrowhead=none color="#533A2210"] - "order-theory.deflationary-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] - "order-theory.deflationary-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - "order-theory.deflationary-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.deflationary-maps-posets" -> "order-theory.deflationary-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.deflationary-maps-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.061519858739629646 shape=circle style=filled width=0.061519858739629646] - "order-theory.deflationary-maps-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.deflationary-maps-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - 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"order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-frames" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-frames" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-frames" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-frames" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-inflattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.059007775570652274 shape=circle style=filled width=0.059007775570652274] - "order-theory.dependent-products-large-inflattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-inflattices" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-inflattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-inflattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-inflattices" -> "order-theory.large-inflattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0629389547650211 shape=circle style=filled width=0.0629389547650211] - "order-theory.dependent-products-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-locales" -> "order-theory.dependent-products-large-frames" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06606824211104302 shape=circle style=filled width=0.06606824211104302] - "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-meet-semilattices" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.dependent-products-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-posets" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-posets" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-posets" -> "order-theory.dependent-products-large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.dependent-products-large-preorders" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-preorders" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] - "order-theory.dependent-products-large-suplattices" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-suplattices" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-suplattices" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-suplattices" -> "order-theory.dependent-products-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.dependent-products-large-suplattices" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.distributive-lattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0606940513737671 shape=circle style=filled width=0.0606940513737671] - "order-theory.distributive-lattices" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.distributive-lattices" -> "order-theory.lattices" [arrowhead=none color="#533A2210"] - "order-theory.distributive-lattices" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.distributive-lattices" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.distributive-lattices" -> "order-theory.join-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.finite-coverings-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.finite-coverings-locales" -> "order-theory.locales" [arrowhead=none color="#533A2210"] - "order-theory.finite-coverings-locales" -> "order-theory.coverings-locales" [arrowhead=none color="#533A2210"] - "order-theory.finite-coverings-locales" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.finite-posets" -> "order-theory.finite-preorders" [arrowhead=none color="#533A2210"] - "order-theory.finite-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.finite-posets" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.finite-posets" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07797910051895961 shape=circle style=filled width=0.07797910051895961] - "order-theory.finite-preorders" -> "order-theory.decidable-subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "univalent-combinatorics.equality-finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "order-theory.decidable-preorders" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "foundation.decidable-equality" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "foundation.decidable-propositions" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "foundation.mere-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "univalent-combinatorics.decidable-subtypes" [arrowhead=none color="#533A2210"] - "order-theory.finite-preorders" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.finite-total-orders" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] - "order-theory.finite-total-orders" -> "foundation.decidable-types" [arrowhead=none color="#533A2210"] - "order-theory.finite-total-orders" -> "order-theory.finite-posets" [arrowhead=none color="#533A2210"] - "order-theory.finite-total-orders" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.finite-total-orders" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.14145108846852988 shape=circle style=filled width=0.14145108846852988] - "order-theory.finitely-graded-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "foundation.embeddings" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "elementary-number-theory.modular-arithmetic" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "foundation.injective-maps" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "foundation.equality-dependent-pair-types" [arrowhead=none color="#533A2210"] - "order-theory.finitely-graded-posets" -> "order-theory.total-orders" [arrowhead=none color="#533A2210"] - 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color="#533A2210"] - "order-theory.frames" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.frames" -> "order-theory.suplattices" [arrowhead=none color="#533A2210"] - "order-theory.frames" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.galois-connections-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.12677669221435825 shape=circle style=filled width=0.12677669221435825] - "order-theory.galois-connections-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.galois-connections-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.galois-connections-large-posets" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.galois-connections-large-posets" -> "order-theory.principal-lower-sets-large-posets" [arrowhead=none color="#533A2210"] - 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"order-theory.homomorphisms-frames" -> "order-theory.homomorphisms-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-frames" -> "order-theory.homomorphisms-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-frames" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.homomorphisms-large-frames" -> "order-theory.large-frames" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-frames" -> "order-theory.homomorphisms-large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-frames" -> "order-theory.homomorphisms-large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.homomorphisms-large-locales" -> "order-theory.homomorphisms-large-frames" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05073057513131416 shape=circle style=filled width=0.05073057513131416] - "order-theory.homomorphisms-large-meet-semilattices" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-meet-semilattices" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.homomorphisms-large-suplattices" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-large-suplattices" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06192863306205975 shape=circle style=filled width=0.06192863306205975] - "order-theory.homomorphisms-meet-semilattices" -> "order-theory.greatest-lower-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-meet-semilattices" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-meet-semilattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-meet-semilattices" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#533A2210"] - "order-theory.homomorphisms-meet-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.homomorphisms-meet-suplattices" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - 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width=0.05] - "order-theory.ideals-preorders" -> "order-theory.lower-types-preorders" [arrowhead=none color="#533A2210"] - "order-theory.ideals-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.ideals-preorders" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] - "order-theory.incidence-algebras" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.incidence-algebras" -> "commutative-algebra.commutative-rings" [arrowhead=none color="#533A2210"] - "order-theory.incidence-algebras" -> "order-theory.locally-finite-posets" [arrowhead=none color="#533A2210"] - "order-theory.incidence-algebras" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.incidence-algebras" -> "order-theory.interval-subposets" [arrowhead=none color="#533A2210"] - "order-theory.incidence-algebras" -> "foundation.inhabited-types" [arrowhead=none color="#533A2210"] - 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color="#533A2210"] - "order-theory.increasing-sequences-posets" -> "order-theory.sequences-posets" [arrowhead=none color="#533A2210"] - "order-theory.inflationary-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] - "order-theory.inflationary-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - "order-theory.inflationary-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.inflationary-maps-posets" -> "order-theory.inflationary-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.inflationary-maps-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0617245842929672 shape=circle style=filled width=0.0617245842929672] - "order-theory.inflationary-maps-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.inflationary-maps-preorders" -> 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color="#533A2210"] - "order-theory.interval-subposets" -> "foundation-core.cartesian-product-types" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.08829760823402076 shape=circle style=filled width=0.08829760823402076] - "order-theory.join-preserving-maps-posets" -> "foundation.small-types" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" -> "foundation.subtype-identity-principle" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" -> "foundation.raising-universe-levels" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" -> "foundation.booleans" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.join-preserving-maps-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - 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color="#533A2210"] - "order-theory.join-semilattices" -> "group-theory.semigroups" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "order-theory.upper-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.join-semilattices" -> "order-theory.least-upper-bounds-posets" [arrowhead=none color="#533A2210"] - "order-theory.joins-finite-families-join-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0832982825080884 shape=circle style=filled width=0.0832982825080884] - "order-theory.joins-finite-families-join-semilattices" -> 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fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.lower-types-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.maximal-chains-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.maximal-chains-posets" -> "order-theory.maximal-chains-preorders" [arrowhead=none color="#533A2210"] - "order-theory.maximal-chains-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.maximal-chains-posets" -> "order-theory.chains-posets" [arrowhead=none color="#533A2210"] - "order-theory.maximal-chains-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.maximal-chains-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.maximal-chains-preorders" -> "order-theory.chains-preorders" [arrowhead=none color="#533A2210"] - 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"order-theory.meet-semilattices" -> "group-theory.isomorphisms-semigroups" [arrowhead=none color="#533A2210"] - "order-theory.meet-suplattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] - "order-theory.meet-suplattices" -> "order-theory.meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.meet-suplattices" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.meet-suplattices" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.meet-suplattices" -> "order-theory.suplattices" [arrowhead=none color="#533A2210"] - "order-theory.meets-finite-families-meet-semilattices" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0811502671200689 shape=circle style=filled width=0.0811502671200689] - "order-theory.meets-finite-families-meet-semilattices" -> "group-theory.commutative-semigroups" [arrowhead=none color="#533A2210"] - 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fillcolor="#533A22" height=0.10572350755845444 shape=circle style=filled width=0.10572350755845444] - "order-theory.nuclei-large-locales" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-frames" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-meet-subsemilattices" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.homomorphisms-large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.nuclei-large-locales" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] - "order-theory.opposite-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-posets" -> "order-theory.opposite-large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-posets" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-posets" -> "foundation.large-identity-types" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-posets" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] - "order-theory.opposite-large-preorders" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-preorders" -> "foundation.large-identity-types" [arrowhead=none color="#533A2210"] - "order-theory.opposite-large-preorders" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05502503444319857 shape=circle style=filled width=0.05502503444319857] - "order-theory.opposite-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - "order-theory.opposite-posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-posets" -> "order-theory.opposite-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.opposite-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.052921383526080924 shape=circle style=filled width=0.052921383526080924] - "order-theory.opposite-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.opposite-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.08344959649748425 shape=circle style=filled width=0.08344959649748425] - "order-theory.order-preserving-maps-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-posets" -> "order-theory.order-preserving-maps-posets" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-posets" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07700228825802675 shape=circle style=filled width=0.07700228825802675] - "order-theory.order-preserving-maps-large-preorders" -> "order-theory.large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-preorders" -> "foundation-core.homotopies" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-preorders" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-large-preorders" -> "order-theory.similarity-of-elements-large-preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07296438524291976 shape=circle style=filled width=0.07296438524291976] - "order-theory.order-preserving-maps-posets" -> "foundation.torsorial-type-families" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-posets" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-posets" -> "order-theory.order-preserving-maps-preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-posets" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07667391879499177 shape=circle style=filled width=0.07667391879499177] - "order-theory.order-preserving-maps-preorders" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" -> "foundation.subtype-identity-principle" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" -> "foundation.homotopy-induction" [arrowhead=none color="#533A2210"] - "order-theory.order-preserving-maps-preorders" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06625891564490792 shape=circle style=filled width=0.06625891564490792] - "order-theory.ordinals" -> "order-theory.well-founded-relations" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" -> "order-theory.posets" [arrowhead=none color="#533A2210"] - "order-theory.ordinals" -> "order-theory.transitive-well-founded-relations" [arrowhead=none color="#533A2210"] - "order-theory.posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.07156780854205468 shape=circle style=filled width=0.07156780854205468] - "order-theory.posets" -> "order-theory.preorders" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "category-theory.precategories" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "category-theory.categories" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "foundation.binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "category-theory.isomorphisms-in-precategories" [arrowhead=none color="#533A2210"] - "order-theory.posets" -> "foundation.injective-maps" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.06625891564490792 shape=circle style=filled width=0.06625891564490792] - "order-theory.powers-of-large-locales" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.large-suplattices" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.dependent-products-large-locales" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.large-locales" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "foundation.large-binary-relations" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.top-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.powers-of-large-locales" -> "order-theory.large-meet-semilattices" [arrowhead=none color="#533A2210"] - "order-theory.precategory-of-decidable-total-orders" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05 shape=circle style=filled width=0.05] - "order-theory.precategory-of-decidable-total-orders" -> "category-theory.full-large-subprecategories" [arrowhead=none color="#533A2210"] - "order-theory.precategory-of-decidable-total-orders" -> "category-theory.large-precategories" 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color="#533A2210"] - "order-theory.principal-lower-sets-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.principal-lower-sets-large-posets" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#533A2210"] - "order-theory.principal-lower-sets-large-posets" -> "order-theory.large-subpreorders" [arrowhead=none color="#533A2210"] - "order-theory.principal-lower-sets-large-posets" -> "order-theory.large-subposets" [arrowhead=none color="#533A2210"] - "order-theory.principal-upper-sets-large-posets" [label="" color="#FFFFFF00" fillcolor="#533A22" height=0.05792893183736719 shape=circle style=filled width=0.05792893183736719] - "order-theory.principal-upper-sets-large-posets" -> "order-theory.large-posets" [arrowhead=none color="#533A2210"] - "order-theory.principal-upper-sets-large-posets" -> "foundation.logical-equivalences" [arrowhead=none color="#533A2210"] - "order-theory.principal-upper-sets-large-posets" -> 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color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.complements-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "foundation.inhabited-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-lower-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.disjoint-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.upper-dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.lower-dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.complements-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "foundation.inhabited-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.real-numbers-from-upper-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.06549289087570129 shape=circle style=filled width=0.06549289087570129] - "real-numbers.similarity-real-numbers" -> "order-theory.large-posets" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "foundation.powersets" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.similarity-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.12826066813621598 shape=circle style=filled width=0.12826066813621598] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.inequality-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.disjunction" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.additive-group-of-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.negation" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.arithmetically-located-dedekind-cuts" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "logic.functoriality-existential-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.large-binary-relations" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.addition-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "group-theory.abelian-groups" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.binary-transport" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.negation-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "foundation.functoriality-disjunction" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.strict-inequality-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.subsets-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.05 shape=circle style=filled width=0.05] - "real-numbers.subsets-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.subsets-real-numbers" -> "foundation.images-subtypes" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.07749223352929716 shape=circle style=filled width=0.07749223352929716] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.rational-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "order-theory.upper-bounds-large-posets" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.inequality-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.positive-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.subsets-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.strict-inequality-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "foundation.empty-types" [arrowhead=none color="#B6687710"] - "real-numbers.suprema-families-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - 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"real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.strict-inequality-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.difference-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.similarity-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "real-numbers.dedekind-real-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.transposition-addition-subtraction-cuts-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" [label="" color="#FFFFFF00" fillcolor="#B66877" height=0.07156780854205468 shape=circle style=filled width=0.07156780854205468] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.truncation-levels" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.addition-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.logical-equivalences" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.existential-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.conjunction" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.positive-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.universal-quantification" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.strict-inequality-rational-numbers" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.powersets" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "foundation.truncated-types" [arrowhead=none color="#B6687710"] - "real-numbers.upper-dedekind-real-numbers" -> "elementary-number-theory.difference-rational-numbers" [arrowhead=none color="#B6687710"] - "reflection.abstractions" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.abstractions" -> "primitives.strings" [arrowhead=none color="#00000010"] - "reflection.arguments" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] - "reflection.boolean-reflection" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.boolean-reflection" -> "foundation-core.coproduct-types" [arrowhead=none color="#00000010"] - "reflection.boolean-reflection" -> "foundation.booleans" [arrowhead=none color="#00000010"] - "reflection.boolean-reflection" -> "foundation-core.empty-types" [arrowhead=none color="#00000010"] - "reflection.boolean-reflection" -> "foundation.decidable-types" [arrowhead=none color="#00000010"] - "reflection.definitions" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.07683827893814787 shape=circle style=filled width=0.07683827893814787] - "reflection.definitions" -> "reflection.literals" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "reflection.abstractions" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "reflection.terms" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "reflection.names" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "lists.lists" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "reflection.arguments" [arrowhead=none color="#00000010"] - "reflection.definitions" -> "foundation.empty-types" [arrowhead=none color="#00000010"] - "reflection.erasing-equality" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.fixity" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.fixity" -> "reflection.names" [arrowhead=none color="#00000010"] - "reflection.fixity" -> "primitives.floats" [arrowhead=none color="#00000010"] - "reflection.fixity" -> "elementary-number-theory.addition-integers" [arrowhead=none color="#00000010"] - "reflection.group-solver" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.10959056763571512 shape=circle style=filled width=0.10959056763571512] - "reflection.group-solver" -> "lists.concatenation-lists" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "group-theory.groups" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "foundation.decidable-types" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "lists.functoriality-lists" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "lists.lists" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "lists.reversing-lists" [arrowhead=none color="#00000010"] - "reflection.group-solver" -> "lists.tuples" [arrowhead=none color="#00000010"] - "reflection.literals" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.literals" -> "primitives.strings" [arrowhead=none color="#00000010"] - "reflection.literals" -> "reflection.metavariables" [arrowhead=none color="#00000010"] - "reflection.literals" -> "primitives.machine-integers" [arrowhead=none color="#00000010"] - "reflection.literals" -> "reflection.names" [arrowhead=none color="#00000010"] - "reflection.literals" -> "primitives.characters" [arrowhead=none color="#00000010"] - "reflection.literals" -> "primitives.floats" [arrowhead=none color="#00000010"] - "reflection.metavariables" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.metavariables" -> "foundation.booleans" [arrowhead=none color="#00000010"] - "reflection.metavariables" -> "primitives.strings" [arrowhead=none color="#00000010"] - "reflection.metavariables" -> "lists.lists" [arrowhead=none color="#00000010"] - "reflection.names" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.05 shape=circle style=filled width=0.05] - "reflection.names" -> "foundation.booleans" [arrowhead=none color="#00000010"] - "reflection.names" -> "primitives.machine-integers" [arrowhead=none color="#00000010"] - "reflection.names" -> "primitives.strings" [arrowhead=none color="#00000010"] - 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width=0.061519858739629646] - "reflection.terms" -> "primitives.strings" [arrowhead=none color="#00000010"] - "reflection.terms" -> "reflection.abstractions" [arrowhead=none color="#00000010"] - "reflection.terms" -> "reflection.literals" [arrowhead=none color="#00000010"] - "reflection.terms" -> "reflection.metavariables" [arrowhead=none color="#00000010"] - "reflection.terms" -> "reflection.names" [arrowhead=none color="#00000010"] - "reflection.terms" -> "lists.lists" [arrowhead=none color="#00000010"] - "reflection.terms" -> "reflection.arguments" [arrowhead=none color="#00000010"] - "reflection.type-checking-monad" [label="" color="#FFFFFF00" fillcolor="#000000" height=0.09477519770089146 shape=circle style=filled width=0.09477519770089146] - "reflection.type-checking-monad" -> "primitives.strings" [arrowhead=none color="#00000010"] - "reflection.type-checking-monad" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#00000010"] - 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color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "group-theory.cores-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "group-theory.submonoids" [arrowhead=none color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "group-theory.precategory-of-groups" [arrowhead=none color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "ring-theory.precategory-of-rings" [arrowhead=none color="#1A127710"] - "ring-theory.groups-of-units-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.07330937243946685 shape=circle style=filled width=0.07330937243946685] - "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.integer-multiples-of-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.cyclic-rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-cyclic-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.homomorphisms-ring-extensions-rational-numbers" -> "ring-theory.ring-extensions-rational-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.10440266230183348 shape=circle style=filled width=0.10440266230183348] - "ring-theory.homomorphisms-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-groups" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.09570244044334736 shape=circle style=filled width=0.09570244044334736] - "ring-theory.homomorphisms-semirings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.homomorphisms-semirings" -> "group-theory.homomorphisms-commutative-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12416245902899892 shape=circle style=filled width=0.12416245902899892] - "ring-theory.ideals-generated-by-subsets-rings" -> "lists.concatenation-lists" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "lists.functoriality-lists" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "lists.lists" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-generated-by-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.12013449149639914 shape=circle style=filled width=0.12013449149639914] - "ring-theory.ideals-rings" -> "group-theory.subgroups-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.binary-transport" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "ring-theory.congruence-relations-rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "group-theory.congruence-relations-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "group-theory.congruence-relations-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-rings" -> "foundation.equivalence-relations" [arrowhead=none color="#1A127710"] - "ring-theory.ideals-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.089855504976604 shape=circle style=filled width=0.089855504976604] 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"ring-theory.integer-multiples-of-elements-rings" -> "group-theory.homomorphisms-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.integer-multiples-of-elements-rings" -> "group-theory.integer-multiples-of-elements-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.integer-multiples-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05727187165992967 shape=circle style=filled width=0.05727187165992967] - "ring-theory.intersections-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" -> "foundation.intersections-subtypes" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" -> "order-theory.greatest-lower-bounds-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.intersections-ideals-semirings" -> "foundation.intersections-subtypes" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-semirings" -> "ring-theory.ideals-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.intersections-ideals-semirings" -> "ring-theory.subsets-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.invariant-basis-property-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.invariant-basis-property-rings" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#1A127710"] - "ring-theory.invariant-basis-property-rings" -> "ring-theory.isomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.invariant-basis-property-rings" -> "ring-theory.dependent-products-rings" [arrowhead=none color="#1A127710"] - "ring-theory.invariant-basis-property-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.invertible-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.11209451736914716 shape=circle style=filled width=0.11209451736914716] - "ring-theory.invertible-elements-rings" -> "group-theory.invertible-elements-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.invertible-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.invertible-elements-rings" -> "foundation.contractible-types" 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color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "ring-theory.right-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "ring-theory.poset-of-right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.joins-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.kernels-of-ring-homomorphisms" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.kernels-of-ring-homomorphisms" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - 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[arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.least-upper-bounds-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.unions-subtypes" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.logical-equivalences" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.galois-connections-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "order-theory.reflective-galois-connections-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.poset-of-left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "lists.functoriality-lists" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "lists.lists" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-generated-by-subsets-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] - "ring-theory.left-ideals-rings" -> "foundation.torsorial-type-families" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-rings" -> "foundation.subtype-identity-principle" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.left-ideals-rings" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#1A127710"] - "ring-theory.local-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.local-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.local-rings" -> "foundation.disjunction" [arrowhead=none color="#1A127710"] - "ring-theory.local-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.08435178051687288 shape=circle style=filled width=0.08435178051687288] - "ring-theory.localizations-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "ring-theory.invertible-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "foundation.fibers-of-maps" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "foundation.contractible-types" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#1A127710"] - "ring-theory.localizations-rings" -> "foundation.contractible-maps" [arrowhead=none color="#1A127710"] - "ring-theory.maximal-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.multiples-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] - "ring-theory.multiples-of-elements-rings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.multiples-of-elements-rings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.multiples-of-elements-rings" -> "group-theory.multiples-of-elements-abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.multiples-of-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.multiplicative-orders-of-units-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.nil-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.nil-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nil-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nil-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nil-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.nil-ideals-rings" -> "ring-theory.nilpotent-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.052682459581144495 shape=circle style=filled width=0.052682459581144495] - "ring-theory.nilpotent-elements-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-rings" -> "ring-theory.nilpotent-elements-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-rings" -> "ring-theory.powers-of-elements-rings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-rings" -> "foundation.existential-quantification" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.055708601453115555 shape=circle style=filled width=0.055708601453115555] - "ring-theory.nilpotent-elements-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-semirings" -> "ring-theory.binomial-theorem-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-semirings" -> "foundation.existential-quantification" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.nilpotent-elements-semirings" -> "ring-theory.powers-of-elements-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-ring-extensions-rational-numbers" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.ring-extensions-rational-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-ring-extensions-rational-numbers" -> "elementary-number-theory.positive-integers" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-ring-extensions-rational-numbers" -> "ring-theory.opposite-rings" [arrowhead=none color="#1A127710"] - "ring-theory.opposite-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.opposite-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.partial-sums-sequences-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.partial-sums-sequences-semirings" -> "ring-theory.sums-of-finite-sequences-of-elements-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.partial-sums-sequences-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.partial-sums-sequences-semirings" -> "lists.sequences" [arrowhead=none color="#1A127710"] - "ring-theory.partial-sums-sequences-semirings" -> "lists.finite-sequences" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-cyclic-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.poset-of-cyclic-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-cyclic-rings" -> "ring-theory.category-of-cyclic-rings" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06373568211054055 shape=circle style=filled width=0.06373568211054055] - "ring-theory.poset-of-ideals-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "order-theory.large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06568523458169381 shape=circle style=filled width=0.06568523458169381] - "ring-theory.poset-of-left-ideals-rings" -> "order-theory.large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-left-ideals-rings" -> "foundation.powersets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-left-ideals-rings" -> "order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-left-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] - 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"order-theory.order-preserving-maps-large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "order-theory.order-preserving-maps-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "order-theory.similarity-of-elements-large-posets" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "order-theory.large-preorders" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "foundation.binary-relations" [arrowhead=none color="#1A127710"] - "ring-theory.poset-of-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.powers-of-elements-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06923831664020327 shape=circle style=filled width=0.06923831664020327] - 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width=0.060901553009402865] - "ring-theory.powers-of-elements-semirings" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.powers-of-elements-semirings" -> "elementary-number-theory.addition-natural-numbers" [arrowhead=none color="#1A127710"] - "ring-theory.powers-of-elements-semirings" -> "group-theory.powers-of-elements-monoids" [arrowhead=none color="#1A127710"] - "ring-theory.powers-of-elements-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.precategory-of-rings" -> "category-theory.large-precategories" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-rings" -> "category-theory.precategories" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-rings" -> "ring-theory.homomorphisms-rings" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-semirings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.05 shape=circle style=filled width=0.05] - "ring-theory.precategory-of-semirings" -> "category-theory.large-precategories" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-semirings" -> "category-theory.precategories" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-semirings" -> "ring-theory.semirings" [arrowhead=none color="#1A127710"] - "ring-theory.precategory-of-semirings" -> "ring-theory.homomorphisms-semirings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] - "ring-theory.products-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" -> "ring-theory.poset-of-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" -> "ring-theory.ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" -> "ring-theory.ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] - "ring-theory.products-left-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" -> "ring-theory.left-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" -> "ring-theory.poset-of-left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" -> "ring-theory.left-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-left-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06333857119089935 shape=circle style=filled width=0.06333857119089935] - "ring-theory.products-right-ideals-rings" -> "ring-theory.subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" -> "ring-theory.products-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" -> "ring-theory.right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" -> "ring-theory.right-ideals-generated-by-subsets-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" -> "ring-theory.poset-of-right-ideals-rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-right-ideals-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - "ring-theory.products-rings" [label="" color="#FFFFFF00" fillcolor="#1A1277" height=0.06587701669662775 shape=circle style=filled width=0.06587701669662775] - "ring-theory.products-rings" -> "group-theory.semigroups" [arrowhead=none color="#1A127710"] - "ring-theory.products-rings" -> "group-theory.groups" [arrowhead=none color="#1A127710"] - "ring-theory.products-rings" -> "group-theory.abelian-groups" [arrowhead=none color="#1A127710"] - "ring-theory.products-rings" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#1A127710"] - "ring-theory.products-rings" -> "ring-theory.rings" [arrowhead=none color="#1A127710"] - 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"species.composition-cauchy-series-species-of-types-in-subuniverses" -> "species.cauchy-series-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.composition-cauchy-series-species-of-types-in-subuniverses" -> "foundation.sigma-closed-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.composition-cauchy-series-species-of-types-in-subuniverses" -> "species.cauchy-composition-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.composition-cauchy-series-species-of-types-in-subuniverses" -> "foundation.global-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.composition-cauchy-series-species-of-types-in-subuniverses" -> "species.cauchy-series-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.composition-cauchy-series-species-of-types-in-subuniverses" -> "species.composition-cauchy-series-species-of-types" [arrowhead=none color="#EDA55F10"] - 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shape=circle style=filled width=0.08929214202502928] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.pi-decompositions" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.pi-decompositions-subuniverse" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.global-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.coproducts-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.coproducts-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.product-decompositions" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "species.dirichlet-products-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.dirichlet-exponentials-species-of-types-in-subuniverses" -> "foundation.univalence" [arrowhead=none color="#EDA55F10"] - 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color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] - "species.pointing-species-of-types" -> "species.species-of-types" [arrowhead=none color="#EDA55F10"] - "species.precategory-of-finite-species" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] - "species.precategory-of-finite-species" -> "species.morphisms-finite-species" [arrowhead=none color="#EDA55F10"] - "species.precategory-of-finite-species" -> "category-theory.large-precategories" [arrowhead=none color="#EDA55F10"] - "species.precategory-of-finite-species" -> "category-theory.precategories" [arrowhead=none color="#EDA55F10"] - "species.precategory-of-finite-species" -> "species.species-of-finite-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types-in-subuniverses" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.06233472681039432 shape=circle style=filled width=0.06233472681039432] - 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"foundation.subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types-in-subuniverses" -> "species.cauchy-products-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types-in-subuniverses" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.0504812833271727 shape=circle style=filled width=0.0504812833271727] - "species.products-cauchy-series-species-of-types" -> "foundation.universal-property-coproduct-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "species.species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "foundation.univalence" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "species.cauchy-series-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "species.cauchy-products-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-cauchy-series-species-of-types" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-finite-inhabited-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] - "species.products-dirichlet-series-species-of-finite-inhabited-types" -> "species.dirichlet-series-species-of-finite-inhabited-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-finite-inhabited-types" -> "species.species-of-finite-inhabited-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "species.dirichlet-series-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.global-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.postcomposition-functions" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "species.dirichlet-products-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "species.species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types-in-subuniverses" -> "foundation.universal-property-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05479528381785756 shape=circle style=filled width=0.05479528381785756] - "species.products-dirichlet-series-species-of-types" -> "foundation.postcomposition-functions" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "species.species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "species.dirichlet-products-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "foundation.univalence" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "species.dirichlet-series-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "foundation.universal-property-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.products-dirichlet-series-species-of-types" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.0798969058180198 shape=circle style=filled width=0.0798969058180198] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.dependent-function-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.contractible-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.small-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.sigma-closed-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.decidable-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.inhabited-finite-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.decidable-propositions" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.sigma-decomposition-subuniverse" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "species.species-of-finite-inhabited-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "species.small-cauchy-composition-species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "foundation.inhabited-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-finite-inhabited-types" -> "univalent-combinatorics.sigma-decompositions" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.09570244044334736 shape=circle style=filled width=0.09570244044334736] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.small-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "species.unit-cauchy-composition-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.contractible-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.subuniverses" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.functoriality-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.type-arithmetic-cartesian-product-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.relaxed-sigma-decompositions" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.functoriality-dependent-function-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "species.cauchy-composition-species-of-types" [arrowhead=none color="#EDA55F10"] - "species.small-cauchy-composition-species-of-types-in-subuniverses" -> "foundation.sigma-closed-subuniverses" [arrowhead=none color="#EDA55F10"] - 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"species.species-of-finite-inhabited-types" -> "species.species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.species-of-finite-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] - "species.species-of-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#EDA55F10"] - "species.species-of-finite-types" -> "species.species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.species-of-inhabited-types" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05 shape=circle style=filled width=0.05] - "species.species-of-inhabited-types" -> "species.species-of-types-in-subuniverses" [arrowhead=none color="#EDA55F10"] - "species.species-of-inhabited-types" -> "foundation.inhabited-types" [arrowhead=none color="#EDA55F10"] - "species.species-of-types-in-subuniverses" [label="" color="#FFFFFF00" fillcolor="#EDA55F" height=0.05985685194678195 shape=circle style=filled 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style=filled width=0.05] - "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09517369363237901 shape=circle style=filled width=0.09517369363237901] - "structured-types.commuting-squares-of-pointed-maps" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-squares-of-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.commuting-triangles-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" 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"structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.contractible-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.contractible-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.contractible-pointed-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.cyclic-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05315923363922938 shape=circle style=filled width=0.05315923363922938] - "structured-types.cyclic-types" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.cyclic-types" -> "foundation.surjective-maps" [arrowhead=none color="#069F6E10"] - "structured-types.cyclic-types" -> "foundation.iterating-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.cyclic-types" -> "structured-types.sets-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.051225519292098586 shape=circle style=filled width=0.051225519292098586] - "structured-types.dependent-products-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-h-spaces" -> "structured-types.dependent-products-pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.dependent-products-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05814630195131898 shape=circle style=filled width=0.05814630195131898] - "structured-types.dependent-products-wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-wild-monoids" -> "structured-types.dependent-products-h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-products-wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06776499241351715 shape=circle style=filled width=0.06776499241351715] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.equivalence-extensionality" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.dependent-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07830199672637511 shape=circle style=filled width=0.07830199672637511] - "structured-types.equivalences-h-spaces" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "structured-types.morphisms-h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05749172610234521 shape=circle style=filled width=0.05749172610234521] - "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" -> "foundation.equivalences-arrows" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.089855504976604 shape=circle style=filled width=0.089855504976604] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.equivalence-extensionality" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.morphisms-types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.equivalences-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09437501914625597 shape=circle style=filled width=0.09437501914625597] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.subtype-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "structured-types.morphisms-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.equivalences-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.faithful-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.faithful-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.faithful-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.faithful-pointed-maps" -> "foundation.faithful-maps" [arrowhead=none color="#069F6E10"] - "structured-types.fibers-of-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.fibers-of-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.fibers-of-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.fibers-of-pointed-maps" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.finite-multiplication-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.finite-multiplication-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.finite-multiplication-magmas" -> "univalent-combinatorics.standard-finite-types" [arrowhead=none color="#069F6E10"] - "structured-types.finite-multiplication-magmas" -> "univalent-combinatorics.counting" [arrowhead=none color="#069F6E10"] - "structured-types.function-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.function-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.function-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.function-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] - "structured-types.function-h-spaces" -> "structured-types.dependent-products-h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.function-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.function-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.function-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.function-wild-monoids" -> "structured-types.dependent-products-wild-monoids" [arrowhead=none color="#069F6E10"] - "structured-types.function-wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.function-wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.function-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07068093650719452 shape=circle style=filled width=0.07068093650719452] - "structured-types.h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation-core.endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "structured-types.noncoherent-h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.evaluation-functions" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] - "structured-types.initial-pointed-type-equipped-with-automorphism" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08375140434156425 shape=circle style=filled width=0.08375140434156425] - "structured-types.initial-pointed-type-equipped-with-automorphism" -> "elementary-number-theory.integers" [arrowhead=none color="#069F6E10"] - "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.iterating-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.initial-pointed-type-equipped-with-automorphism" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.initial-pointed-type-equipped-with-automorphism" -> "structured-types.pointed-types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07973885045884406 shape=circle style=filled width=0.07973885045884406] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.symmetric-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "structured-types.constant-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.equality-dependent-function-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.constant-maps" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.binary-transport" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-type-of-h-space-structures" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.involutive-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.involutive-types" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "lists.lists" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms" -> "structured-types.cartesian-products-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-pointed-cartesian-product-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.iterated-pointed-cartesian-product-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-pointed-cartesian-product-types" -> "lists.lists" [arrowhead=none color="#069F6E10"] - "structured-types.iterated-pointed-cartesian-product-types" -> "structured-types.pointed-cartesian-product-types" [arrowhead=none color="#069F6E10"] - "structured-types.magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.magmas" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] - "structured-types.medial-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06006724574819957 shape=circle style=filled width=0.06006724574819957] - "structured-types.medial-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.medial-magmas" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.medial-magmas" -> "structured-types.morphisms-magmas" [arrowhead=none color="#069F6E10"] - "structured-types.medial-magmas" -> "structured-types.product-magmas" [arrowhead=none color="#069F6E10"] - "structured-types.medial-magmas" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06192863306205975 shape=circle style=filled width=0.06192863306205975] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.subtype-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "structured-types.equivalences-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.mere-equivalences-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08999579468728597 shape=circle style=filled width=0.08999579468728597] - "structured-types.morphisms-h-spaces" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-h-spaces" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.morphisms-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.11790860453923727 shape=circle style=filled width=0.11790860453923727] - "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.whiskering-pointed-2-homotopies-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.morphisms-arrows" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation-core.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation-core.homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.commuting-squares-of-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-pointed-arrows" -> "structured-types.commuting-squares-of-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-twisted-pointed-arrows" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05339602427059343 shape=circle style=filled width=0.05339602427059343] - "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-twisted-pointed-arrows" -> "foundation.morphisms-twisted-arrows" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-twisted-pointed-arrows" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05943383002455521 shape=circle style=filled width=0.05943383002455521] - "structured-types.morphisms-types-equipped-with-automorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-automorphisms" -> "structured-types.morphisms-types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06213201171482271 shape=circle style=filled width=0.06213201171482271] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.commuting-squares-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-types-equipped-with-endomorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05195909628863885 shape=circle style=filled width=0.05195909628863885] - "structured-types.morphisms-wild-monoids" -> "structured-types.morphisms-h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-wild-monoids" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-wild-monoids" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] - "structured-types.morphisms-wild-monoids" -> "group-theory.homomorphisms-semigroups" [arrowhead=none color="#069F6E10"] - "structured-types.noncoherent-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.noncoherent-h-spaces" -> "foundation.unital-binary-operations" [arrowhead=none color="#069F6E10"] - "structured-types.noncoherent-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.opposite-pointed-spans" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.opposite-pointed-spans" -> "structured-types.pointed-spans" [arrowhead=none color="#069F6E10"] - "structured-types.opposite-pointed-spans" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.12221670009868099 shape=circle style=filled width=0.12221670009868099] - "structured-types.pointed-2-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.uniform-pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-2-homotopies" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-cartesian-product-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.0587935905605436 shape=circle style=filled width=0.0587935905605436] - "structured-types.pointed-cartesian-product-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-cartesian-product-types" -> "foundation.equality-cartesian-product-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-cartesian-product-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-dependent-functions" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-dependent-functions" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-dependent-functions" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-dependent-functions" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-dependent-pair-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-dependent-pair-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-dependent-pair-types" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.14162935078056077 shape=circle style=filled width=0.14162935078056077] - "structured-types.pointed-equivalences" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.whiskering-pointed-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.injective-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.universal-property-pointed-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.sections" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.fibers-of-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.embeddings" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.pointed-retractions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.contractible-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.transposition-identifications-along-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.precomposition-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.retractions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "foundation.univalence" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-equivalences" -> "structured-types.postcomposition-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-families-of-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-families-of-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.12273173272218177 shape=circle style=filled width=0.12273173272218177] - "structured-types.pointed-homotopies" -> "foundation.action-on-higher-identifications-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation-core.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-homotopies" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09881552504494161 shape=circle style=filled width=0.09881552504494161] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.logical-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-retractions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.contractible-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "structured-types.pointed-sections" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.retractions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-isomorphisms" -> "foundation.sections" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.060485837890913385 shape=circle style=filled width=0.060485837890913385] - "structured-types.pointed-maps" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-maps" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-maps" -> "foundation.action-on-identifications-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-maps" -> "foundation.constant-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06701618498259604 shape=circle style=filled width=0.06701618498259604] - "structured-types.pointed-retractions" -> "foundation-core.contractible-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "foundation-core.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "foundation-core.retractions" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-retractions" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-sections" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-sections" -> "foundation.sections" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-sections" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-sections" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-sections" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08083874863001829 shape=circle style=filled width=0.08083874863001829] - "structured-types.pointed-span-diagrams" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-span-diagrams" -> "structured-types.pointed-spans" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-span-diagrams" -> "foundation.morphisms-arrows" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-span-diagrams" -> "structured-types.morphisms-pointed-arrows" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-span-diagrams" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-spans" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05386648291374754 shape=circle style=filled width=0.05386648291374754] - "structured-types.pointed-spans" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-spans" -> "foundation.spans" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-spans" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06978279409393069 shape=circle style=filled width=0.06978279409393069] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.homotopy-induction" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.fundamental-theorem-of-identity-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types-equipped-with-automorphisms" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-unit-type" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.pointed-unit-type" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-unit-type" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-unit-type" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.055934600764264826 shape=circle style=filled width=0.055934600764264826] - "structured-types.pointed-universal-property-contractible-types" -> "foundation.torsorial-type-families" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "foundation.type-arithmetic-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "foundation.universal-property-contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.pointed-universal-property-contractible-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.postcomposition-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.postcomposition-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.postcomposition-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.precomposition-pointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.precomposition-pointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.precomposition-pointed-maps" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.product-magmas" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.product-magmas" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.sets-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.sets-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.small-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.06273819203736863 shape=circle style=filled width=0.06273819203736863] - "structured-types.small-pointed-types" -> "foundation.small-types" [arrowhead=none color="#069F6E10"] - "structured-types.small-pointed-types" -> "structured-types.pointed-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.small-pointed-types" -> "foundation.contractible-types" [arrowhead=none color="#069F6E10"] - "structured-types.small-pointed-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.small-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-elements-involutive-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.symmetric-elements-involutive-types" -> "univalent-combinatorics.2-element-types" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-elements-involutive-types" -> "structured-types.involutive-types" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-h-spaces" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.symmetric-h-spaces" -> "structured-types.symmetric-elements-involutive-types" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-h-spaces" -> "foundation.symmetric-operations" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-h-spaces" -> "structured-types.involutive-type-of-h-space-structures" [arrowhead=none color="#069F6E10"] - "structured-types.symmetric-h-spaces" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.transposition-pointed-span-diagrams" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.transposition-pointed-span-diagrams" -> "structured-types.pointed-span-diagrams" [arrowhead=none color="#069F6E10"] - "structured-types.transposition-pointed-span-diagrams" -> "structured-types.opposite-pointed-spans" [arrowhead=none color="#069F6E10"] - "structured-types.types-equipped-with-automorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.types-equipped-with-automorphisms" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.types-equipped-with-automorphisms" -> "structured-types.types-equipped-with-endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.types-equipped-with-endomorphisms" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.types-equipped-with-endomorphisms" -> "foundation.endomorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08943331546025578 shape=circle style=filled width=0.08943331546025578] - "structured-types.uniform-pointed-homotopies" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "foundation.structure-identity-principle" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#069F6E10"] - "structured-types.uniform-pointed-homotopies" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.universal-property-pointed-equivalences" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.universal-property-pointed-equivalences" -> "structured-types.precomposition-pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.universal-property-pointed-equivalences" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.universal-property-pointed-equivalences" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.unpointed-maps" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.unpointed-maps" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.08405212848450323 shape=circle style=filled width=0.08405212848450323] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.whiskering-homotopies-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "foundation.path-algebra" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-2-homotopies-concatenation" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09596572138218783 shape=circle style=filled width=0.09596572138218783] - "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.commuting-triangles-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.commuting-squares-of-identifications" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.whiskering-pointed-homotopies-composition" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.09410728805605297 shape=circle style=filled width=0.09410728805605297] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-2-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-maps" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-families-of-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.discrete-reflexive-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.uniform-pointed-homotopies" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.large-transitive-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "wild-category-theory.noncoherent-omega-precategories" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.transitive-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "wild-category-theory.noncoherent-large-omega-precategories" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "structured-types.pointed-dependent-functions" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "foundation.whiskering-identifications-concatenation" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.large-reflexive-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-category-of-pointed-types" -> "globular-types.large-globular-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-groups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.wild-groups" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.wild-groups" -> "structured-types.wild-monoids" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05171572681821669 shape=circle style=filled width=0.05171572681821669] - "structured-types.wild-loops" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" -> "structured-types.wild-quasigroups" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.wild-loops" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.wild-monoids" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.07416481997178037 shape=circle style=filled width=0.07416481997178037] - "structured-types.wild-monoids" -> "structured-types.h-spaces" [arrowhead=none color="#069F6E10"] - "structured-types.wild-monoids" -> "structured-types.pointed-types" [arrowhead=none color="#069F6E10"] - "structured-types.wild-quasigroups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.wild-quasigroups" -> "foundation.automorphisms" [arrowhead=none color="#069F6E10"] - "structured-types.wild-quasigroups" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "structured-types.wild-quasigroups" -> "foundation.binary-equivalences" [arrowhead=none color="#069F6E10"] - "structured-types.wild-semigroups" [label="" color="#FFFFFF00" fillcolor="#069F6E" height=0.05 shape=circle style=filled width=0.05] - "structured-types.wild-semigroups" -> "structured-types.magmas" [arrowhead=none color="#069F6E10"] - "synthetic-category-theory.cone-diagrams-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.12262889924562415 shape=circle style=filled width=0.12262889924562415] - "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "synthetic-category-theory.cospans-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.cone-diagrams-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.cospans-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.10183348601026346 shape=circle style=filled width=0.10183348601026346] - "synthetic-category-theory.cospans-synthetic-categories" -> "synthetic-category-theory.equivalences-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.cospans-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.cospans-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.equivalences-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.06510649876675342 shape=circle style=filled width=0.06510649876675342] - "synthetic-category-theory.equivalences-synthetic-categories" -> "synthetic-category-theory.sections-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.equivalences-synthetic-categories" -> "synthetic-category-theory.retractions-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.equivalences-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.equivalences-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.invertible-functors-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.09490821558768603 shape=circle style=filled width=0.09490821558768603] - "synthetic-category-theory.invertible-functors-synthetic-categories" -> "synthetic-category-theory.sections-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.invertible-functors-synthetic-categories" -> "synthetic-category-theory.retractions-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.invertible-functors-synthetic-categories" -> "synthetic-category-theory.equivalences-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.invertible-functors-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.invertible-functors-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.pullbacks-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.08479927320887588 shape=circle style=filled width=0.08479927320887588] - "synthetic-category-theory.pullbacks-synthetic-categories" -> "synthetic-category-theory.equivalences-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.pullbacks-synthetic-categories" -> "synthetic-category-theory.cospans-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.pullbacks-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.pullbacks-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.pullbacks-synthetic-categories" -> "synthetic-category-theory.cone-diagrams-synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.retractions-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.05 shape=circle style=filled width=0.05] - "synthetic-category-theory.retractions-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.retractions-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.sections-synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.05 shape=circle style=filled width=0.05] - "synthetic-category-theory.sections-synthetic-categories" -> "synthetic-category-theory.synthetic-categories" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.sections-synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-category-theory.synthetic-categories" [label="" color="#FFFFFF00" fillcolor="#2FEABE" height=0.16545678037860773 shape=circle style=filled width=0.16545678037860773] - "synthetic-category-theory.synthetic-categories" -> "globular-types.globular-types" [arrowhead=none color="#2FEABE10"] - "synthetic-homotopy-theory.0-acyclic-maps" [label="" color="#FFFFFF00" fillcolor="#B0D45A" height=0.05 shape=circle style=filled width=0.05] - "synthetic-homotopy-theory.0-acyclic-maps" -> "foundation.surjective-maps" [arrowhead=none color="#B0D45A10"] - "synthetic-homotopy-theory.0-acyclic-maps" -> "foundation.truncation-levels" [arrowhead=none color="#B0D45A10"] - 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color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "elementary-number-theory.multiplication-natural-numbers" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.decidable-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "univalent-combinatorics.equality-standard-finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.negation" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.decidable-propositions" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.orientations-complete-undirected-graph" -> "foundation.mere-equivalences" [arrowhead=none 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color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.contractible-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.functoriality-dependent-pair-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.maybe" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.truncated-pi-finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.untruncated-pi-finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.set-truncations" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.retracts-of-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.dependent-function-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.equality-coproduct-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.finitely-truncated-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.counting" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.truncation-levels" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.retracts-of-finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "univalent-combinatorics.finitely-many-connected-components" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pi-finite-types" -> "foundation.conjunction" [arrowhead=none color="#F70D6110"] - 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"univalent-combinatorics.embeddings-standard-finite-types" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "foundation.injective-maps" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "foundation.whiskering-homotopies-composition" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "foundation.noninjective-maps" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "foundation.negation" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "elementary-number-theory.strict-inequality-natural-numbers" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "foundation.negated-equality" [arrowhead=none color="#F70D6110"] - "univalent-combinatorics.pigeonhole-principle" -> "univalent-combinatorics.repetitions-of-values" [arrowhead=none color="#F70D6110"] - 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"wild-category-theory.maps-noncoherent-omega-precategories" -> "globular-types.globular-maps" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" [label="" color="#FFFFFF00" fillcolor="#E2C12E" height=0.09557052798858454 shape=circle style=filled width=0.09557052798858454] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.large-transitive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "wild-category-theory.noncoherent-omega-precategories" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.transitive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "category-theory.precategories" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.large-reflexive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-large-omega-precategories" -> "globular-types.large-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" [label="" color="#FFFFFF00" fillcolor="#E2C12E" height=0.0832982825080884 shape=circle style=filled width=0.0832982825080884] - "wild-category-theory.noncoherent-omega-precategories" -> "globular-types.reflexive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" -> "globular-types.transitive-globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" -> "foundation.strictly-involutive-identity-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" -> "category-theory.precategories" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" -> "globular-types.globular-types" [arrowhead=none color="#E2C12E10"] - "wild-category-theory.noncoherent-omega-precategories" -> "foundation.action-on-identifications-binary-functions" [arrowhead=none color="#E2C12E10"] -} From 6083c9c31a351d9ef7bde1c9ec10bb4dbea8c745 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:50:22 +0200 Subject: [PATCH 10/13] a few too many parentheses --- .../coproduct-decompositions-subuniverse.lagda.md | 7 +++---- src/foundation/product-decompositions-subuniverse.lagda.md | 4 ++-- 2 files changed, 5 insertions(+), 6 deletions(-) diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index a86fec7fd1..494082f580 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -302,7 +302,7 @@ module _ equiv-postcomp-equiv ( commutative-coproduct) ( inclusion-subuniverse P X))) ∘e - ( ( inv-associative-Σ))) + ( inv-associative-Σ)) ``` ### Equivalence between iterated coproduct and ternary coproduct decomposition @@ -499,7 +499,6 @@ module _ ( eq-is-prop is-property-is-empty))) ( ( raise-empty l1 , C1) , is-empty-raise-empty)) ∘e ( ( inv-associative-Σ) ∘e - ( ( equiv-tot (λ _ → commutative-product)) ∘e - ( ( associative-Σ))))))) ∘e - ( ( associative-Σ)) + ( equiv-tot (λ _ → commutative-product) ∘e associative-Σ))))) ∘e + ( associative-Σ) ``` diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index 56db0b71c8..fa89797005 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -376,6 +376,6 @@ module _ is-contr-raise-unit)) ∘e ( ( inv-associative-Σ) ∘e ( ( equiv-tot (λ _ → commutative-product)) ∘e - ( ( associative-Σ)))))))) ∘e - ( ( associative-Σ))) + ( associative-Σ))))))) ∘e + ( associative-Σ)) ``` From f793998335a2cc62625940d3a347fb3dac81a718 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 1 Sep 2025 23:53:10 +0200 Subject: [PATCH 11/13] missed one --- src/univalent-combinatorics/2-element-subtypes.lagda.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/univalent-combinatorics/2-element-subtypes.lagda.md b/src/univalent-combinatorics/2-element-subtypes.lagda.md index 9c1bd2707d..09ce8a50b9 100644 --- a/src/univalent-combinatorics/2-element-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-subtypes.lagda.md @@ -126,7 +126,7 @@ module _ Fin 2 ≃ type-standard-2-Element-Subtype equiv-type-standard-2-Element-Subtype = ( inv-equiv - ( left-distributive-Σ-coproduct (type-Set X) (Id x) (Id y))) ∘e + ( left-distributive-Σ-coproduct)) ∘e ( equiv-coproduct ( equiv-is-contr ( is-contr-Fin-1) From 3d17aacd4847a1a7e696cae5fc12306504f63f79 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Sat, 13 Sep 2025 00:27:13 +0200 Subject: [PATCH 12/13] Update functors-set-magmoids.lagda.md --- src/category-theory/functors-set-magmoids.lagda.md | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index 19c562a888..5007025482 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -231,10 +231,8 @@ module _ equiv-eq-map-eq-functor-Set-Magmoid = equiv-ap-emb ( comp-emb - ( emb-subtype - ( preserves-comp-hom-prop-map-Set-Magmoid A B)) - ( emb-equiv - ( inv-associative-Σ))) + ( emb-subtype (preserves-comp-hom-prop-map-Set-Magmoid A B)) + ( emb-equiv inv-associative-Σ)) eq-map-eq-functor-Set-Magmoid : F = G → map-functor-Set-Magmoid A B F = map-functor-Set-Magmoid A B G From f8213a5720bf196bdc145cdf1db6b24e060f82ec Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Sat, 13 Sep 2025 00:27:52 +0200 Subject: [PATCH 13/13] Update functors-precategories.lagda.md --- src/category-theory/functors-precategories.lagda.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index d80d8fbe24..5c3f902d6a 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -278,7 +278,7 @@ module _ equiv-ap-emb ( comp-emb ( emb-subtype (is-functor-prop-map-Precategory C D)) - ( emb-equiv (inv-associative-Σ))) + ( emb-equiv inv-associative-Σ)) eq-map-eq-functor-Precategory : (F = G) → (map-functor-Precategory C D F = map-functor-Precategory C D G)