diff --git a/PackageInfo.g b/PackageInfo.g
index 0cd3c90..db25b63 100644
--- a/PackageInfo.g
+++ b/PackageInfo.g
@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "FinSetsForCAP",
 Subtitle := "The elementary topos of (skeletal) finite sets",
-Version := "2023.10-01",
+Version := "2023.10-02",
 
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
@@ -98,7 +98,7 @@ PackageDoc := rec(
 Dependencies := rec(
   GAP := ">= 4.12.1",
   NeededOtherPackages := [
-                   [ "CAP", ">= 2023.09-11" ],
+                   [ "CAP", ">= 2023.10-07" ],
                    [ "CartesianCategories", ">= 2023.08-13" ],
                    [ "Toposes", ">= 2023.10-01" ],
                    ],
diff --git a/examples/PrecompileCategoryOfSkeletalFinSetsWithMorphismsGivenByLists.g b/examples/PrecompileCategoryOfSkeletalFinSetsWithMorphismsGivenByLists.g
index dd0ac45..9076c5a 100644
--- a/examples/PrecompileCategoryOfSkeletalFinSetsWithMorphismsGivenByLists.g
+++ b/examples/PrecompileCategoryOfSkeletalFinSetsWithMorphismsGivenByLists.g
@@ -8,7 +8,7 @@
 
 LoadPackage( "FinSetsForCAP", false );
 #! true
-LoadPackage( "CompilerForCAP", false );
+LoadPackage( "CompilerForCAP", ">= 2023.10-03", false );
 #! true
 
 ReadPackage( "FinSetsForCAP", "gap/CompilerLogic.gi" );
@@ -25,6 +25,7 @@ primitive_operations :=
 list_of_operations :=
   SortedList( Concatenation( primitive_operations, [
           "CoastrictionToImage",
+          "CoimageProjection",
           "IsHomSetInhabited",
           "TruthMorphismOfImplies",
           #"HasPushoutComplement",
diff --git a/gap/SkeletalFinSets.gi b/gap/SkeletalFinSets.gi
index d1cfb35..e36a329 100644
--- a/gap/SkeletalFinSets.gi
+++ b/gap/SkeletalFinSets.gi
@@ -481,6 +481,22 @@ AddImageEmbedding( SkeletalFinSets,
     
 end );
 
+##
+AddAstrictionToCoimage( SkeletalFinSets,
+  function ( cat, phi )
+    local L, map;
+    
+    L := AsList( phi );
+    
+    ## unlike ImageObject which is a subobject of the range,
+    ## the CoimageObject is a factor object of the source,
+    ## and we want to retain the sorting of the source:
+    map := DuplicateFreeList( L );
+    
+    return MorphismConstructor( cat, ObjectConstructor( cat, BigInt( Length( map ) ) ), map, Range( phi ) );
+    
+end );
+
 ## Limits
 
 ##
diff --git a/gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi b/gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi
index 6abe118..4ab6a2c 100644
--- a/gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi
+++ b/gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi
@@ -5,6 +5,19 @@
 #
 BindGlobal( "ADD_FUNCTIONS_FOR_SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled", function ( cat )
     
+    ##
+    AddAstrictionToCoimage( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_1_1;
+    deduped_1_1 := DuplicateFreeList( AsList( alpha_1 ) );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Length, BigInt( Length( deduped_1_1 ) ) ), Range( alpha_1 ), AsList, deduped_1_1 );
+end
+########
+        
+    , 100 );
+    
     ##
     AddCartesianBraidingInverseWithGivenDirectProducts( cat,
         
@@ -184,6 +197,23 @@ end
         
     , 100 );
     
+    ##
+    AddCoimageProjection( cat,
+        
+########
+function ( cat_1, alpha_1 )
+    local deduped_3_1, deduped_4_1, deduped_5_1;
+    deduped_5_1 := AsList( alpha_1 );
+    deduped_4_1 := Source( alpha_1 );
+    deduped_3_1 := DuplicateFreeList( deduped_5_1 );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, deduped_4_1, CreateCapCategoryObjectWithAttributes( cat_1, Length, BigInt( Length( deduped_3_1 ) ) ), AsList, List( [ 0 .. Length( deduped_4_1 ) - 1 ], function ( x_2 )
+              return -1 + BigInt( SafePosition( deduped_3_1, deduped_5_1[(1 + x_2)] ) );
+          end ) );
+end
+########
+        
+    , 202 : IsPrecompiledDerivation := true );
+    
     ##
     AddColift( cat,