installed ExactCoverWithGlobalElements primitively

and used it to "derive" MorphismsOfExternalHom

Author: mohamed-barakat

PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "FinSetsForCAP",
 Subtitle := "The elementary topos of (skeletal) finite sets",
-Version := "2023.05-05",
+Version := "2023.05-06",
 
 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",

gap/SkeletalFinSetsForCAP.gi

@@ -857,25 +857,34 @@ AddCartesianLambdaIntroduction( SkeletalFinSets,
 
 end );
 
+##
+AddExactCoverWithGlobalElements( SkeletalFinSets,
+  function ( cat, A )
+    local T;
+    
+    T := TerminalObject( cat );
+    
+    return List( [ 0 .. Length( A ) - 1 ], i -> MapOfFinSets( cat, T, [ i ], A ) );
+    
+end );
+
 ##
 AddExponentialOnMorphismsWithGivenExponentials( SkeletalFinSets,
   function ( cat, S, alpha, beta, T )
-    local M, m, N, n, D, MN;
+    local M, N, MN, mors;
 
     M := Range( alpha );
-    m := Length( M );
     N := Source( beta );
-    n := Length( N );
-    
-    D := TerminalObject( cat );
 
     MN := ExponentialOnObjects( cat, M, N );
+
+    mors := ExactCoverWithGlobalElements( cat, MN );
 
     return MapOfFinSets(
               cat,
               S,
-              List( [ 0 .. n ^ m - 1 ],
-                function ( i )
+              List( mors,
+                function ( mor )
                   return
                     AsList( CartesianLambdaIntroduction( cat,
                             PreComposeList(
@@ -884,17 +893,14 @@ AddExponentialOnMorphismsWithGivenExponentials( SkeletalFinSets,
                                       CartesianLambdaElimination( cat,
                                               M,
                                               N,
-                                              MapOfFinSets( cat,
-                                                      D,
-                                                      [ i ],
-                                                      MN ) ),
+                                              mor ),
                                       beta ] ) ) )[1 + 0];
 
               end ),
               T );
 
-end, 1 + Sum( [ [ "TerminalObject", 1 ],
-                [ "ExponentialOnObjects", 1 ],
+end, 1 + Sum( [ [ "ExponentialOnObjects", 1 ],
+                [ "ExactCoverWithGlobalElements", 1 ],
                 [ "PreComposeList", 2 ],
                 [ "CartesianLambdaElimination", 2 ],
                 [ "CartesianLambdaIntroduction", 2 ] ],
@@ -965,27 +971,22 @@ end );
 ##
 AddMorphismsOfExternalHom( SkeletalFinSets,
   function ( cat, A, B )
-    local hom_A_B, T;
+    local hom_A_B, mors;
 
     hom_A_B := ExponentialOnObjects( cat, A, B );
 
-    T := TerminalObject( cat );
+    mors := ExactCoverWithGlobalElements( cat, hom_A_B );
 
-    return List( hom_A_B,
-                 i -> CartesianLambdaElimination( cat,
+    return List( mors,
+                 mor -> CartesianLambdaElimination( cat,
                          A,
                          B,
-                         MapOfFinSets( cat, T, [ i ], hom_A_B ) ) );
+                         mor ) );
 
-end );
-
-##
-AddExactCoverWithGlobalElements( SkeletalFinSets,
-  function ( cat, A )
-    
-    return MorphismsOfExternalHom( cat, TerminalObject( cat ), A );
-    
-end );
+end, 1 + Sum( [ [ "ExponentialOnObjects", 1 ],
+                [ "ExactCoverWithGlobalElements", 1 ],
+                [ "CartesianLambdaElimination", 2 ] ],
+        e -> e[2] * CurrentOperationWeight( SkeletalFinSets!.derivations_weight_list, e[1] ) ) );
 
 end );
 

gap/precompiled_categories/CategoryOfSkeletalFinSetsPrecompiled.gi

@@ -285,11 +285,10 @@ end
 
 ########
 function ( cat_1, arg2_1 )
-    local hoisted_2_1, deduped_3_1;
-    deduped_3_1 := Length( arg2_1 );
-    hoisted_2_1 := CreateCapCategoryObjectWithAttributes( cat_1, Length, BigInt( 1 ) );
-    return List( [ 0 .. deduped_3_1 - 1 ], function ( i_2 )
-            return CreateCapCategoryMorphismWithAttributes( cat_1, hoisted_2_1, arg2_1, AsList, [ REM_INT( i_2, deduped_3_1 ) ] );
+    local hoisted_1_1;
+    hoisted_1_1 := CreateCapCategoryObjectWithAttributes( cat_1, Length, BigInt( 1 ) );
+    return List( [ 0 .. Length( arg2_1 ) - 1 ], function ( i_2 )
+            return CreateCapCategoryMorphismWithAttributes( cat_1, hoisted_1_1, arg2_1, AsList, [ i_2 ] );
         end );
 end
 ########
@@ -309,10 +308,10 @@ function ( cat_1, s_1, alpha_1, beta_1, r_1 )
     hoisted_4_1 := AsList( beta_1 );
     hoisted_3_1 := AsList( alpha_1 );
     hoisted_2_1 := [ 0 .. deduped_8_1 - 1 ];
-    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, AsList, List( [ 0 .. deduped_7_1 ^ deduped_8_1 - 1 ], function ( i_2 )
+    return CreateCapCategoryMorphismWithAttributes( cat_1, s_1, r_1, AsList, List( [ 0 .. deduped_7_1 ^ deduped_8_1 - 1 ], function ( logic_new_func_x_2 )
               local hoisted_1_2;
               hoisted_1_2 := List( hoisted_2_1, function ( i_3 )
-                      return REM_INT( QUO_INT( i_2, deduped_7_1 ^ i_3 ), deduped_7_1 );
+                      return REM_INT( QUO_INT( logic_new_func_x_2, deduped_7_1 ^ i_3 ), deduped_7_1 );
                   end );
               return Sum( List( hoisted_6_1, function ( k_3 )
                         return hoisted_4_1[(1 + hoisted_1_2[(1 + hoisted_3_1[(1 + CAP_JIT_INCOMPLETE_LOGIC( k_3 ))])])] * hoisted_5_1 ^ k_3;
@@ -651,15 +650,15 @@ function ( cat_1, arg2_1, arg3_1 )
     deduped_4_1 := Length( arg2_1 );
     deduped_3_1 := Length( arg3_1 );
     hoisted_2_1 := [ 0 .. deduped_4_1 - 1 ];
-    return List( [ 0 .. deduped_3_1 ^ deduped_4_1 - 1 ], function ( i_2 )
+    return List( [ 0 .. deduped_3_1 ^ deduped_4_1 - 1 ], function ( logic_new_func_x_2 )
             return CreateCapCategoryMorphismWithAttributes( cat_1, arg2_1, arg3_1, AsList, List( hoisted_2_1, function ( i_3 )
-                      return REM_INT( QUO_INT( i_2, deduped_3_1 ^ i_3 ), deduped_3_1 );
+                      return REM_INT( QUO_INT( logic_new_func_x_2, deduped_3_1 ^ i_3 ), deduped_3_1 );
                   end ) );
         end );
 end
 ########
 
-    , 100 );
+    , 401 );
 
     ##
     AddObjectConstructor( cat,