@@ -51,7 +51,7 @@ InstallMethod( CategoryOfSkeletalFinSets,
5151end );
5252
5353# #
54- InstallMethodForCompilerForCAP ( FinSetOp,
54+ InstallMethod ( FinSetOp,
5555 [ IsCategoryOfSkeletalFinSets, IsBigInt ] ,
5656
5757 function ( cat, n )
@@ -96,7 +96,7 @@ InstallMethod( MapOfFinSets,
9696end );
9797
9898# #
99- InstallOtherMethodForCompilerForCAP ( MapOfFinSets,
99+ InstallOtherMethod ( MapOfFinSets,
100100 " for a category of skeletal finite sets, two CAP skeletal finite sets and a list" ,
101101 [ IsCategoryOfSkeletalFinSets, IsSkeletalFiniteSet, IsList, IsSkeletalFiniteSet ] ,
102102
@@ -343,7 +343,7 @@ end );
343343AddIdentityMorphism( SkeletalFinSets,
344344 function ( cat, n )
345345
346- return MapOfFinSets ( cat, n, [ 0 .. Length( n ) - 1 ] , n );
346+ return MorphismConstructor ( cat, n, [ 0 .. Length( n ) - 1 ] , n );
347347
348348end );
349349
@@ -360,15 +360,15 @@ AddPreCompose( SkeletalFinSets,
360360
361361 cmp := List( s, i -> im_post[ 1 + im_pre[ 1 + i]] );
362362
363- return MapOfFinSets ( cat, s, cmp, t );
363+ return MorphismConstructor ( cat, s, cmp, t );
364364
365365end );
366366
367367# #
368368AddImageObject( SkeletalFinSets,
369369 function ( cat, phi )
370370
371- return FinSet ( cat, BigInt( Length( Set( AsList( phi ) ) ) ) );
371+ return ObjectConstructor ( cat, BigInt( Length( Set( AsList( phi ) ) ) ) );
372372
373373end );
374374
@@ -446,7 +446,7 @@ AddLift( SkeletalFinSets,
446446 gg := AsList( g );
447447 ff := AsList( f );
448448
449- return MapOfFinSets ( cat, S, List( S, x -> - 1 + BigInt( SafePosition( gg, ff[ 1 + x] ) ) ), T );
449+ return MorphismConstructor ( cat, S, List( S, x -> - 1 + BigInt( SafePosition( gg, ff[ 1 + x] ) ) ), T );
450450
451451end );
452452
@@ -482,15 +482,15 @@ AddColift( SkeletalFinSets,
482482 return gg[ SafePosition( ff, y )] ;
483483 end ;
484484
485- return MapOfFinSets ( cat, S, List( S, y -> chi(y) ), T );
485+ return MorphismConstructor ( cat, S, List( S, y -> chi(y) ), T );
486486
487487end );
488488
489489# #
490490AddImageEmbeddingWithGivenImageObject( SkeletalFinSets,
491491 function ( cat, phi, image )
492492
493- return MapOfFinSets ( cat, image, Set( AsList( phi ) ), Range( phi ) );
493+ return MorphismConstructor ( cat, image, Set( AsList( phi ) ), Range( phi ) );
494494
495495end );
496496
@@ -507,7 +507,7 @@ AddCoastrictionToImageWithGivenImageObject( SkeletalFinSets,
507507
508508 L := List( s, i -> - 1 + BigInt( SafePosition( images, G[ 1 + i] ) ) );
509509
510- pi := MapOfFinSets ( cat, s, L, image_object );
510+ pi := MorphismConstructor ( cat, s, L, image_object );
511511
512512 # % CAP_JIT_DROP_NEXT_STATEMENT
513513 Assert ( 3 , IsEpimorphism( cat, pi ) );
@@ -531,23 +531,23 @@ end );
531531AddTerminalObject( SkeletalFinSets,
532532 function ( cat )
533533
534- return FinSet ( cat, BigInt( 1 ) );
534+ return ObjectConstructor ( cat, BigInt( 1 ) );
535535
536536end );
537537
538538# #
539539AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject( SkeletalFinSets,
540540 function ( cat, m, t )
541541
542- return MapOfFinSets ( cat, m, ListWithIdenticalEntries( Length( m ), BigInt( 0 ) ), t );
542+ return MorphismConstructor ( cat, m, ListWithIdenticalEntries( Length( m ), BigInt( 0 ) ), t );
543543
544544end );
545545
546546# #
547547AddDirectProduct( SkeletalFinSets,
548548 function ( cat, L )
549549
550- return FinSet ( cat, Product( List( L, Length ) ) );
550+ return ObjectConstructor ( cat, Product( List( L, Length ) ) );
551551
552552end );
553553
@@ -562,7 +562,7 @@ AddProjectionInFactorOfDirectProductWithGivenDirectProduct( SkeletalFinSets,
562562
563563 a := Product( List( D{[ 1 .. k - 1 ]} , Length ) );
564564
565- return MapOfFinSets ( cat, P, List( P, i -> RemInt( QuoInt( i, a ), l ) ), T );
565+ return MorphismConstructor ( cat, P, List( P, i -> RemInt( QuoInt( i, a ), l ) ), T );
566566
567567end );
568568
@@ -580,7 +580,7 @@ AddUniversalMorphismIntoDirectProductWithGivenDirectProduct( SkeletalFinSets,
580580 taus := List( tau, AsList );
581581
582582 # if l = 0, then Sum( [ 0 .. l - 1 ], j -> ... ) = 0 ∈ TerminalObject = P
583- return MapOfFinSets ( cat, T, List( T, i -> Sum( [ 0 .. l - 1 ] , j -> taus[ 1 + j][ 1 + i] * dd[ 1 + j] ) ), P );
583+ return MorphismConstructor ( cat, T, List( T, i -> Sum( [ 0 .. l - 1 ] , j -> taus[ 1 + j][ 1 + i] * dd[ 1 + j] ) ), P );
584584
585585end );
586586
@@ -593,7 +593,7 @@ AddEqualizer( SkeletalFinSets,
593593
594594 Eq := Filtered( [ 0 .. Length( s ) - 1 ] , x -> ForAll( [ 1 .. Length( D ) - 1 ] , j -> D2[ j][ 1 + x] = D2[ j + 1 ][ 1 + x] ) );
595595
596- return FinSet ( cat, Length( Eq ) );
596+ return ObjectConstructor ( cat, Length( Eq ) );
597597
598598end );
599599
@@ -606,7 +606,7 @@ AddEmbeddingOfEqualizerWithGivenEqualizer( SkeletalFinSets,
606606
607607 Eq := Filtered( [ 0 .. Length( s ) - 1 ] , x -> ForAll( [ 1 .. Length( D ) - 1 ] , j -> D2[ j][ 1 + x] = D2[ j + 1 ][ 1 + x] ) );
608608
609- return MapOfFinSets ( cat, E, Eq, s );
609+ return MorphismConstructor ( cat, E, Eq, s );
610610
611611end );
612612
@@ -621,7 +621,7 @@ AddUniversalMorphismIntoEqualizerWithGivenEqualizer( SkeletalFinSets,
621621
622622 t := AsList( tau );
623623
624- return MapOfFinSets ( cat, test_object, List( test_object, x -> - 1 + BigInt( SafePosition( Eq, t[ 1 + x] ) ) ), E );
624+ return MorphismConstructor ( cat, test_object, List( test_object, x -> - 1 + BigInt( SafePosition( Eq, t[ 1 + x] ) ) ), E );
625625
626626end );
627627
@@ -640,15 +640,15 @@ end );
640640AddInitialObject( SkeletalFinSets,
641641 function ( cat )
642642
643- return FinSet ( cat, BigInt( 0 ) );
643+ return ObjectConstructor ( cat, BigInt( 0 ) );
644644
645645end );
646646
647647# #
648648AddUniversalMorphismFromInitialObjectWithGivenInitialObject( SkeletalFinSets,
649649 function ( cat, m, I )
650650
651- return MapOfFinSets ( cat, I, [ ] , m );
651+ return MorphismConstructor ( cat, I, [ ] , m );
652652
653653end );
654654
@@ -692,15 +692,15 @@ end );
692692AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject( SkeletalFinSets,
693693 function ( cat, M, injective_object )
694694
695- return MapOfFinSets ( cat, M, [ 0 .. Length( M ) - 1 ] , injective_object );
695+ return MorphismConstructor ( cat, M, [ 0 .. Length( M ) - 1 ] , injective_object );
696696
697697end );
698698
699699# #
700700AddCoproduct( SkeletalFinSets,
701701 function ( cat, L )
702702
703- return FinSet ( cat, Sum( List( L, Length ) ) );
703+ return ObjectConstructor ( cat, Sum( List( L, Length ) ) );
704704
705705end );
706706
@@ -715,7 +715,7 @@ AddInjectionOfCofactorOfCoproductWithGivenCoproduct( SkeletalFinSets,
715715
716716 s := L[ i] ;
717717
718- return MapOfFinSets ( cat, s, [ sum .. sum + Length( s ) - 1 ] , coproduct );
718+ return MorphismConstructor ( cat, s, [ sum .. sum + Length( s ) - 1 ] , coproduct );
719719
720720end );
721721
@@ -726,15 +726,15 @@ AddUniversalMorphismFromCoproductWithGivenCoproduct( SkeletalFinSets,
726726
727727 concat := Concatenation( List( tau, AsList ) );
728728
729- return MapOfFinSets ( cat, S, concat, test_object );
729+ return MorphismConstructor ( cat, S, concat, test_object );
730730
731731end );
732732
733733# #
734734AddCoequalizer( SkeletalFinSets,
735735 function ( cat, s, D )
736736
737- return FinSet ( cat, BigInt( Length( SKELETAL_FIN_SETS_ExplicitCoequalizer( s, D ) ) ) );
737+ return ObjectConstructor ( cat, BigInt( Length( SKELETAL_FIN_SETS_ExplicitCoequalizer( s, D ) ) ) );
738738
739739end );
740740
@@ -747,7 +747,7 @@ AddProjectionOntoCoequalizerWithGivenCoequalizer( SkeletalFinSets,
747747
748748 cmp := List( s, x -> - 1 + BigInt( SafeUniquePositionProperty( Cq, c -> x in c ) ) );
749749
750- return MapOfFinSets ( cat, s, cmp, C );
750+ return MorphismConstructor ( cat, s, cmp, C );
751751
752752end );
753753
@@ -758,7 +758,7 @@ AddUniversalMorphismFromCoequalizerWithGivenCoequalizer( SkeletalFinSets,
758758
759759 Cq := SKELETAL_FIN_SETS_ExplicitCoequalizer( s, D );
760760
761- return MapOfFinSets ( cat, C, List( Cq, x -> tau( x[ 1 ] ) ), Range( tau ) );
761+ return MorphismConstructor ( cat, C, List( Cq, x -> tau( x[ 1 ] ) ), Range( tau ) );
762762
763763end );
764764
@@ -805,7 +805,7 @@ AddCartesianBraidingInverseWithGivenDirectProducts( SkeletalFinSets,
805805
806806 n := Length( N );
807807
808- return MapOfFinSets ( cat, MN, List( MN , i -> RemInt( i, n ) * m + QuoInt( i, n ) ), NM );
808+ return MorphismConstructor ( cat, MN, List( MN , i -> RemInt( i, n ) * m + QuoInt( i, n ) ), NM );
809809
810810end );
811811
@@ -817,7 +817,7 @@ AddExponentialOnObjects( SkeletalFinSets,
817817 m := Length( M );
818818 n := Length( N );
819819
820- return FinSet ( cat, n ^ m );
820+ return ObjectConstructor ( cat, n ^ m );
821821
822822end );
823823
@@ -831,7 +831,7 @@ AddCartesianLambdaElimination( SkeletalFinSets,
831831
832832 v := AsList( intro )[ 1 ] ;
833833
834- return MapOfFinSets ( cat,
834+ return MorphismConstructor ( cat,
835835 M,
836836 List( [ 0 .. m - 1 ] , i -> RemInt( QuoInt( v, n^ i ), n ) ),
837837 N );
@@ -850,7 +850,7 @@ AddCartesianLambdaIntroduction( SkeletalFinSets,
850850
851851 images := AsList( map );
852852
853- return MapOfFinSets ( cat,
853+ return MorphismConstructor ( cat,
854854 TerminalObject( cat ),
855855 [ Sum( List( [ 0 .. m - 1 ] , k -> images[ 1 + k] * n^ k ) ) ] ,
856856 ExponentialOnObjects( cat, M, N ) );
@@ -864,7 +864,7 @@ AddExactCoverWithGlobalElements( SkeletalFinSets,
864864
865865 T := TerminalObject( cat );
866866
867- return List( [ 0 .. Length( A ) - 1 ] , i -> MapOfFinSets ( cat, T, [ i ] , A ) );
867+ return List( [ 0 .. Length( A ) - 1 ] , i -> MorphismConstructor ( cat, T, [ i ] , A ) );
868868
869869end );
870870
@@ -880,7 +880,7 @@ AddExponentialOnMorphismsWithGivenExponentials( SkeletalFinSets,
880880
881881 mors := ExactCoverWithGlobalElements( cat, MN );
882882
883- return MapOfFinSets ( cat,
883+ return MorphismConstructor ( cat,
884884 S,
885885 List( mors, mor ->
886886 AsList( CartesianLambdaIntroduction( cat,
@@ -911,7 +911,7 @@ AddCartesianEvaluationMorphismWithGivenSource( SkeletalFinSets,
911911
912912 exp := n ^ m;
913913
914- return MapOfFinSets ( cat, HM_NxM, List( [ 0 .. ( n^ m * m ) - 1 ] , i -> RemInt( QuoInt( i, n^ QuoInt( i, exp ) ), n ) ), N );
914+ return MorphismConstructor ( cat, HM_NxM, List( [ 0 .. ( n^ m * m ) - 1 ] , i -> RemInt( QuoInt( i, n^ QuoInt( i, exp ) ), n ) ), N );
915915
916916end );
917917
@@ -925,17 +925,17 @@ AddCartesianCoevaluationMorphismWithGivenRange( SkeletalFinSets,
925925
926926 mn := m * n;
927927
928- # return MapOfFinSets ( cat, M, List( [ 0 .. m - 1 ], i -> Sum( [ 0 .. n - 1 ], j -> ( i + m * j ) * (m*n)^j ) ), HN_MxN );
928+ # return MorphismConstructor ( cat, M, List( [ 0 .. m - 1 ], i -> Sum( [ 0 .. n - 1 ], j -> ( i + m * j ) * (m*n)^j ) ), HN_MxN );
929929
930- return MapOfFinSets ( cat, M, List( [ 0 .. m - 1 ] , i -> i * GeometricSum( mn, n ) + m * mn * GeometricSumDiff1( mn, n ) ), HN_MxN );
930+ return MorphismConstructor ( cat, M, List( [ 0 .. m - 1 ] , i -> i * GeometricSum( mn, n ) + m * mn * GeometricSumDiff1( mn, n ) ), HN_MxN );
931931
932932end );
933933
934934# #
935935AddSubobjectClassifier( SkeletalFinSets,
936936 function ( cat )
937937
938- return FinSet ( cat, BigInt( 2 ) );
938+ return ObjectConstructor ( cat, BigInt( 2 ) );
939939
940940end );
941941
@@ -959,7 +959,7 @@ AddClassifyingMorphismOfSubobjectWithGivenSubobjectClassifier( SkeletalFinSets,
959959
960960 end );
961961
962- return MapOfFinSets ( cat, range, chi, Omega );
962+ return MorphismConstructor ( cat, range, chi, Omega );
963963
964964end );
965965
@@ -991,7 +991,7 @@ InstallMethod( String,
991991 [ IsSkeletalFiniteSet ] ,
992992
993993 function ( s )
994- return Concatenation( " FinSet ( SkeletalFinSets, " , String( Length( s ) ), " )" );
994+ return Concatenation( " ObjectConstructor ( SkeletalFinSets, " , String( Length( s ) ), " )" );
995995end );
996996
997997# #
@@ -1000,7 +1000,7 @@ InstallMethod( String,
10001000 [ IsSkeletalFiniteSetMap ] ,
10011001
10021002 function ( phi )
1003- return Concatenation( " MapOfFinSets ( SkeletalFinSets, " , String( Source( phi ) ), " , " , String( AsList( phi ) ), " , " , String( Range( phi ) ), " )" );
1003+ return Concatenation( " MorphismConstructor ( SkeletalFinSets, " , String( Source( phi ) ), " , " , String( AsList( phi ) ), " , " , String( Range( phi ) ), " )" );
10041004end );
10051005
10061006# #
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