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link to initiality implies induction
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plt-amy committed Dec 19, 2024
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Expand Up @@ -55,11 +55,13 @@ unique among functions with these properties.
x f x ≡ map-out p r x
```

By a standard categorical argument, existence and uniqueness together give us an
By a [standard categorical argument], existence and uniqueness together give us an
*induction principle* for the integers: to construct a section of a type family
$P : \bb{Z} \to \ty$, it is enough to give an element of $P(0)$ and a family of
equivalences $P(n) \simeq P(n + 1)$.

[standard categorical argument]: Data.Wellfounded.W.html#initial-algebras-are-inductive-types

```agda
ℤ-η : z map-out point rotate z ≡ z
ℤ-η z = sym (map-out-unique id refl (λ _ refl) z)
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