AddCoimageProjection

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

Author: mohamed-barakat

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" );

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 );
+
 ##
 AddCoastrictionToImageWithGivenImageObject( SkeletalFinSets,
   function ( cat, phi, image_object )

gap/precompiled_categories/SkeletalCategoryOfFiniteSetsWithMorphismsGivenByListsPrecompiled.gi

@@ -184,6 +184,23 @@ 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,