AddCoimageProjection

ImageObject( phi )   ⤳ Set
CoimageObject( phi ) ⤳ DuplicateFreeList

and compiled AstrictionToCoimage

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",

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" );
@@ -24,6 +24,7 @@ primitive_operations :=
           category_constructor( : no_precompiled_code := true ) );;
 list_of_operations :=
   SortedList( Concatenation( primitive_operations, [
+          "AstrictionToCoimage",
           "CoastrictionToImage",
           "IsHomSetInhabited",
           "TruthMorphismOfImplies",

gap/SkeletalFinSets.gi

@@ -481,6 +481,25 @@ AddImageEmbedding( SkeletalFinSets,
 
 end );
 
+##
+AddCoimageProjection( SkeletalFinSets,
+  function ( cat, phi )
+    local L, imgs, 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 source
+    imgs := DuplicateFreeList( L );
+
+    map := List( [ 0 .. Length( Source( phi ) ) - 1 ], i ->
+                 -1 + SafePosition( imgs, L[1 + i] ) );
+
+    return MorphismConstructor( cat, Source( phi ), map, ObjectConstructor( cat, BigInt( Length( imgs ) ) ) );
+
+end );
+
 ## Limits
 
 ##

gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi

@@ -5,6 +5,32 @@
 #
 BindGlobal( "ADD_FUNCTIONS_FOR_SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled", function ( cat )
 
+    ##
+    AddAstrictionToCoimage( cat,
+
+########
+function ( cat_1, alpha_1 )
+    local deduped_3_1, hoisted_4_1, deduped_5_1, deduped_6_1, deduped_7_1;
+    deduped_7_1 := AsList( alpha_1 );
+    deduped_6_1 := DuplicateFreeList( deduped_7_1 );
+    deduped_5_1 := BigInt( Length( deduped_6_1 ) );
+    hoisted_4_1 := BigInt( 0 );
+    deduped_3_1 := List( [ 0 .. Length( Source( alpha_1 ) ) - 1 ], function ( i_2 )
+            return -1 + SafePosition( deduped_6_1, deduped_7_1[(1 + i_2)] );
+        end );
+    return CreateCapCategoryMorphismWithAttributes( cat_1, CreateCapCategoryObjectWithAttributes( cat_1, Length, deduped_5_1 ), Range( alpha_1 ), AsList, List( [ 0 .. deduped_5_1 - 1 ], function ( y_2 )
+              if not y_2 in deduped_3_1 then
+                  return hoisted_4_1;
+              else
+                  return deduped_7_1[SafePosition( deduped_3_1, y_2 )];
+              fi;
+              return;
+          end ) );
+end
+########
+
+    , 202 : IsPrecompiledDerivation := true );
+
     ##
     AddCartesianBraidingInverseWithGivenDirectProducts( cat,
 
@@ -184,6 +210,23 @@ 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 ( i_2 )
+              return -1 + SafePosition( deduped_3_1, deduped_5_1[(1 + i_2)] );
+          end ) );
+end
+########
+
+    , 100 );
+
     ##
     AddColift( cat,