CoequalizerMorphisms -> CoequalizerAutomorphisms and altered output

Author: mohamed-barakat

examples/SkeletalCategoryOfTransitiveLeftGSets.g

@@ -104,8 +104,8 @@ Print( DotVertexLabelledDigraph( digraph ) );
 #! 2 -> 4
 #! 3 -> 4
 #! }
-ForAll( objs, o -> o = Coequalizer( Omega1,
-        List( CoequalizerMorphisms( o ), g -> g / TS3 ) ) );
+ForAll( objs, o -> o = CoequalizerOfIdentityAndAutomorphisms( Omega1,
+        List( CoequalizerAutomorphisms( o ), g -> g / TS3 ) ) );
 #! true
 
 #! @EndExample

gap/SkeletalCategoryOfTransitiveLeftGSets.gd

@@ -160,11 +160,11 @@ DeclareAttribute( "Size",
 
 #! @Description
 #!  The input is a transitive left $G$-set <A>Omega</A> $\cong G / U_i$.
-#!  The output is the list of endomorphisms of the principal $G$-set $G / U_1$ defined by the generators of $U_i$.
-#!  The coequalizers of these morphisms is the input object <A>Omega</A> $\cong G / U_i$.
+#!  The output is the list of automorphisms of the principal $G$-set $G / U_1$ defined by the generators of $U_i$.
+#!  The coequalizers of the identity and these automorphisms is the input object <A>Omega</A> $\cong G / U_i$.
 #! @Arguments Omega
 #! @Returns a list of morphisms
-DeclareAttribute( "CoequalizerMorphisms",
+DeclareAttribute( "CoequalizerAutomorphisms",
         IsObjectInSkeletalCategoryOfTransitiveLeftGSets );
 
 DeclareAttribute( "EmbeddingOfUnderlyingGroupAsCategoryData",

gap/SkeletalCategoryOfTransitiveLeftGSets.gi

@@ -513,7 +513,7 @@ InstallMethod( Size,
 end );
 
 ##
-InstallOtherMethodForCompilerForCAP( CoequalizerMorphisms,
+InstallOtherMethodForCompilerForCAP( CoequalizerAutomorphisms,
         "for the skeletal category of transitive left G-sets and a transitive left G-set therein",
         [ IsSkeletalCategoryOfTransitiveLeftGSets, IsObjectInSkeletalCategoryOfTransitiveLeftGSets ],
 
@@ -526,7 +526,7 @@ InstallOtherMethodForCompilerForCAP( CoequalizerMorphisms,
 
     U := RepresentativesOfSubgroupsUpToConjugation( SkeletalTransitiveGSets );
 
-    gs := Concatenation( [ One( UnderlyingGroup( SkeletalTransitiveGSets ) ) ], GeneratorsOfGroup( U[ObjectNumber( Omega )] ) );
+    gs := GeneratorsOfGroup( U[ObjectNumber( Omega )] );
 
     return List( gs, g ->
                  MorphismConstructor( G_as_cat,
@@ -537,13 +537,13 @@ InstallOtherMethodForCompilerForCAP( CoequalizerMorphisms,
 end );
 
 ##
-InstallMethod( CoequalizerMorphisms,
+InstallMethod( CoequalizerAutomorphisms,
         "for a skeletal transitive left G-set",
         [ IsObjectInSkeletalCategoryOfTransitiveLeftGSets ],
 
   function ( Omega )
 
-    return CoequalizerMorphisms( CapCategory( Omega ), Omega );
+    return CoequalizerAutomorphisms( CapCategory( Omega ), Omega );
 
 end );
 
@@ -609,25 +609,25 @@ InstallMethodForCompilerForCAP( ExtendFunctorToSkeletalCategoryOfTransitiveLeftG
       function ( obj_in_SkeletalTransitiveGSets )
         local coeq_mors, diagram, coeq;
 
-        coeq_mors := CoequalizerMorphisms( SkeletalTransitiveGSets, obj_in_SkeletalTransitiveGSets );
+        coeq_mors := CoequalizerAutomorphisms( SkeletalTransitiveGSets, obj_in_SkeletalTransitiveGSets );
 
         diagram := List( coeq_mors, g ->
                          functor_on_morphisms(
                                  img_obj,
                                  g,
                                  img_obj ) );
 
-        return Coequalizer( category_with_coequalizers, img_obj, diagram );
+        return CoequalizerOfIdentityAndAutomorphisms( category_with_coequalizers, img_obj, diagram );
 
     end;
 
     extended_functor_on_morphisms :=
       function ( source, mor_in_SkeletalTransitiveGSets, target )
         local coeq_mors_source, coeq_mors_target, diagram_source, diagram_target, g;
 
-        coeq_mors_source := CoequalizerMorphisms( SkeletalTransitiveGSets, Source( mor_in_SkeletalTransitiveGSets ) );
+        coeq_mors_source := CoequalizerAutomorphisms( SkeletalTransitiveGSets, Source( mor_in_SkeletalTransitiveGSets ) );
 
-        coeq_mors_target := CoequalizerMorphisms( SkeletalTransitiveGSets, Target( mor_in_SkeletalTransitiveGSets ) );
+        coeq_mors_target := CoequalizerAutomorphisms( SkeletalTransitiveGSets, Target( mor_in_SkeletalTransitiveGSets ) );
 
         diagram_source := List( coeq_mors_source, g ->
                                 functor_on_morphisms(
@@ -641,19 +641,19 @@ InstallMethodForCompilerForCAP( ExtendFunctorToSkeletalCategoryOfTransitiveLeftG
                                         g,
                                         img_obj ) );
 
-        if not IsEqualForObjects( category_with_coequalizers, source, Coequalizer( category_with_coequalizers, diagram_source ) ) then
+        if not IsEqualForObjects( category_with_coequalizers, source, CoequalizerOfIdentityAndAutomorphisms( category_with_coequalizers, img_obj, diagram_source ) ) then
             # COVERAGE_IGNORE_NEXT_LINE
             Error( "source and Coequalizer( diagram_source ) do not coincide\n" );
         fi;
 
-        if not IsEqualForObjects( category_with_coequalizers, target, Coequalizer( category_with_coequalizers, diagram_target ) ) then
+        if not IsEqualForObjects( category_with_coequalizers, target, CoequalizerOfIdentityAndAutomorphisms( category_with_coequalizers, img_obj, diagram_target ) ) then
             # COVERAGE_IGNORE_NEXT_LINE
             Error( "target and Coequalizer( diagram_target ) do not coincide\n" );
         fi;
 
         g := GroupAsCategoryMorphism( G_as_cat, UnderlyingGroupElement( mor_in_SkeletalTransitiveGSets ) );
 
-        return CoequalizerFunctorialWithGivenCoequalizers( category_with_coequalizers,
+        return CoequalizerOfIdentityAndAutomorphismsFunctorialWithGivenCoequalizers( category_with_coequalizers,
                        source,
                        diagram_source,
                        functor_on_morphisms(

tst/coequalizer.tst

@@ -17,7 +17,7 @@ gap> Omega1 := TS5.1;
 S5 / U_1
 gap> Omega3 := TS5.3;
 S5 / U_3
-gap> ForAll( objs, o -> o = Coequalizer( Omega1, List( CoequalizerMorphisms( o ), g -> g / TS5 ) ) );
+gap> ForAll( objs, o -> o = CoequalizerOfIdentityAndAutomorphisms( Omega1, List( CoequalizerAutomorphisms( o ), g -> g / TS5 ) ) );
 true
 gap> mors := SetOfMorphisms( TS5 );; Length( mors );
 681