diff --git a/gap/CompilerLogic.gi b/gap/CompilerLogic.gi
index 22011ba..bf18aaa 100644
--- a/gap/CompilerLogic.gi
+++ b/gap/CompilerLogic.gi
@@ -88,7 +88,7 @@ end );
 ## Teach CompilerForCAP about the input type of the function so it can correctly type the function,
 ## that can be done with the following code (adapted from the existing List type signature):
 ##
-CapJitAddTypeSignature( "List", [ IsSkeletalFiniteSet, IsFunction ], function ( args, func_stack )
+CapJitAddTypeSignature( "List", [ IsObjectInCategoryOfSkeletalFinSets, IsFunction ], function ( args, func_stack )
     
     args := ShallowCopy( args );
     
@@ -109,7 +109,7 @@ end );
 CapJitAddLogicTemplate(
     rec(
         variable_names := [ "M", "func" ],
-        variable_filters := [ IsSkeletalFiniteSet, IsObject ],
+        variable_filters := [ IsObjectInCategoryOfSkeletalFinSets, IsObject ],
         src_template := "List( M, func )",
         dst_template := "List( [ 0 .. Length( M ) - 1 ], func )",
     )
diff --git a/gap/Julia.gi b/gap/Julia.gi
index ef26785..8b1e543 100644
--- a/gap/Julia.gi
+++ b/gap/Julia.gi
@@ -33,7 +33,7 @@ end );
 
 ##
 InstallMethod( MapOfFinSets,
-        [ IsSkeletalFiniteSet, IsJuliaObject, IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets, IsJuliaObject, IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( source, graph, range )
     
diff --git a/gap/SkeletalFinSets.gd b/gap/SkeletalFinSets.gd
index 17fe281..6279abe 100644
--- a/gap/SkeletalFinSets.gd
+++ b/gap/SkeletalFinSets.gd
@@ -19,14 +19,14 @@ DeclareCategory( "IsCategoryOfSkeletalFinSets",
 #! The GAP category of objects in the category
 #! of skeletal finite sets.
 #! @Arguments object
-DeclareCategory( "IsSkeletalFiniteSet",
+DeclareCategory( "IsObjectInCategoryOfSkeletalFinSets",
                  IsCapCategoryObject );
 
 #! @Description
 #! The GAP category of morphisms in the category
 #! of skeletal finite sets.
 #! @Arguments object
-DeclareCategory( "IsSkeletalFiniteSetMap",
+DeclareCategory( "IsMorphismInCategoryOfSkeletalFinSets",
                  IsCapCategoryMorphism );
 
 #! @Section Attributes
@@ -37,9 +37,9 @@ DeclareCategory( "IsSkeletalFiniteSetMap",
 #! @Arguments M
 #! @Returns an integer
 DeclareAttribute( "Length",
-        IsSkeletalFiniteSet );
+        IsObjectInCategoryOfSkeletalFinSets );
 
-CapJitAddTypeSignature( "Length", [ IsSkeletalFiniteSet ], IsBigInt );
+CapJitAddTypeSignature( "Length", [ IsObjectInCategoryOfSkeletalFinSets ], IsBigInt );
 
 #! @Description
 #!  The list associated to a skeletal finite set, i.e.,
@@ -47,18 +47,18 @@ CapJitAddTypeSignature( "Length", [ IsSkeletalFiniteSet ], IsBigInt );
 #! @Arguments M
 #! @Returns a list
 DeclareAttribute( "AsList",
-        IsSkeletalFiniteSet );
+        IsObjectInCategoryOfSkeletalFinSets );
 
-CapJitAddTypeSignature( "AsList", [ IsSkeletalFiniteSet ], rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) );
+CapJitAddTypeSignature( "AsList", [ IsObjectInCategoryOfSkeletalFinSets ], rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) );
 
 #! @Description
-#!  The graph defining the skeletal finite set morphism <A>phi</A>, see <Ref Oper="MapOfFinSets" Label="for IsSkeletalFiniteSet, IsList, IsSkeletalFiniteSet" />.
+#!  The graph defining the skeletal finite set morphism <A>phi</A>, see <Ref Oper="MapOfFinSets" Label="for IsObjectInCategoryOfSkeletalFinSets, IsList, IsObjectInCategoryOfSkeletalFinSets" />.
 #! @Arguments phi
 #! @Returns a list
 DeclareAttribute( "AsList",
-        IsSkeletalFiniteSetMap );
+        IsMorphismInCategoryOfSkeletalFinSets );
 
-CapJitAddTypeSignature( "AsList", [ IsSkeletalFiniteSetMap ], rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) );
+CapJitAddTypeSignature( "AsList", [ IsMorphismInCategoryOfSkeletalFinSets ], rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) );
 
 #! @Section Constructors
 
@@ -97,7 +97,7 @@ KeyDependentOperation( "FinSet", IsCategoryOfSkeletalFinSets, IsBigInt, ReturnTr
 #! @Arguments s, G, t
 #! @Returns a &CAP; morphism
 DeclareOperation( "MapOfFinSets",
-        [ IsSkeletalFiniteSet, IsList, IsSkeletalFiniteSet ] );
+        [ IsObjectInCategoryOfSkeletalFinSets, IsList, IsObjectInCategoryOfSkeletalFinSets ] );
 #! @InsertChunk  SkeletalMapOfFinSets
 
 #! @Section Tools
@@ -107,7 +107,7 @@ DeclareOperation( "MapOfFinSets",
 #! @Arguments s, f
 #! @Returns a list
 DeclareOperation( "ListOp",
-        [ IsSkeletalFiniteSet, IsFunction ] );
+        [ IsObjectInCategoryOfSkeletalFinSets, IsFunction ] );
 
 #! @Description
 #!  Construct the embedding $\iota:$<A>s</A>$\to$<A>t</A> of the finite sets <A>s</A> and <A>t</A>,
@@ -115,34 +115,34 @@ DeclareOperation( "ListOp",
 #! @Arguments s, t
 #! @Returns a &CAP; morphism
 DeclareOperation( "EmbeddingOfFinSets",
-        [ IsSkeletalFiniteSet, IsSkeletalFiniteSet ] );
+        [ IsObjectInCategoryOfSkeletalFinSets, IsObjectInCategoryOfSkeletalFinSets ] );
 
 #! @Description
 #!  Compute the Preimage of <A>t</A> under the morphism <A>phi</A>.
 #! @Arguments phi, t
 #! @Returns a &CAP; object
 DeclareOperation( "Preimage",
-        [ IsSkeletalFiniteSetMap, IsList ] );
+        [ IsMorphismInCategoryOfSkeletalFinSets, IsList ] );
 
 #! @Description
 #!  Compute the image of <A>s_</A> under the morphism <A>phi</A>.
 #! @Arguments phi, s_
 #! @Returns a &CAP; object
 DeclareOperation( "ImageObject",
-        [ IsSkeletalFiniteSetMap, IsSkeletalFiniteSet ] );
+        [ IsMorphismInCategoryOfSkeletalFinSets, IsObjectInCategoryOfSkeletalFinSets ] );
 
 #! @Description
 #!  Returns the image of <C><A>L</A>[1]</C> under the map <A>phi</A> assuming <C><A>L</A>[1]</C> is a nonnegative integer smaller than <C>Length( Source( <A>phi</A> ) )</C>.
 #! @Arguments phi, L
 #! @Returns a list
 # DeclareOperation( "CallFuncList",
-#         [ IsSkeletalFiniteSetMap, IsList ] );
+#         [ IsMorphismInCategoryOfSkeletalFinSets, IsList ] );
 
 # Technical functions
 DeclareGlobalFunction( "INSTALL_FUNCTIONS_FOR_SKELETAL_FIN_SETS" );
 
 DeclareGlobalFunction( "SKELETAL_FIN_SETS_ExplicitCoequalizer" );
-CapJitAddTypeSignature( "SKELETAL_FIN_SETS_ExplicitCoequalizer", [ IsSkeletalFiniteSet, IsList ], rec( filter := IsList, element_type := rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) ) );
+CapJitAddTypeSignature( "SKELETAL_FIN_SETS_ExplicitCoequalizer", [ IsObjectInCategoryOfSkeletalFinSets, IsList ], rec( filter := IsList, element_type := rec( filter := IsList, element_type := rec( filter := IsBigInt ) ) ) );
 
 DeclareGlobalFunction( "SKELETAL_FIN_SETS_IsMonomorphism" );
 CapJitAddTypeSignature( "SKELETAL_FIN_SETS_IsMonomorphism", [ IsList, IsBigInt ], IsBool );
diff --git a/gap/SkeletalFinSets.gi b/gap/SkeletalFinSets.gi
index f5708fd..dc6fe79 100644
--- a/gap/SkeletalFinSets.gi
+++ b/gap/SkeletalFinSets.gi
@@ -13,7 +13,7 @@ InstallMethod( CategoryOfSkeletalFinSets,
     
     cat := CreateCapCategoryWithDataTypes(
         "SkeletalFinSets", IsCategoryOfSkeletalFinSets,
-        IsSkeletalFiniteSet, IsSkeletalFiniteSetMap, IsCapCategoryTwoCell,
+        IsObjectInCategoryOfSkeletalFinSets, IsMorphismInCategoryOfSkeletalFinSets, IsCapCategoryTwoCell,
         IsBigInt, rec( filter := IsList, element_type := rec( filter := IsBigInt ) ), fail
     );
     
@@ -63,7 +63,7 @@ end );
 ##
 InstallMethod( AsList,
         "for a CAP skeletal finite set",
-        [ IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s )
     
@@ -74,7 +74,7 @@ end );
 ##
 InstallMethod( ListOp,
         "for a CAP skeletal finite set and a function",
-        [ IsSkeletalFiniteSet, IsFunction ],
+        [ IsObjectInCategoryOfSkeletalFinSets, IsFunction ],
         
   function ( s, f )
     
@@ -87,7 +87,7 @@ end );
 ##
 InstallMethod( MapOfFinSets,
         "for two CAP skeletal finite sets and a list",
-        [ IsSkeletalFiniteSet, IsList, IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets, IsList, IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s, G, t )
     
@@ -98,7 +98,7 @@ end );
 ##
 InstallOtherMethod( MapOfFinSets,
         "for a category of skeletal finite sets, two CAP skeletal finite sets and a list",
-        [ IsCategoryOfSkeletalFinSets, IsSkeletalFiniteSet, IsList, IsSkeletalFiniteSet ],
+        [ IsCategoryOfSkeletalFinSets, IsObjectInCategoryOfSkeletalFinSets, IsList, IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( cat, s, G, t )
     
@@ -109,7 +109,7 @@ end );
 ##
 InstallMethod( EmbeddingOfFinSets,
         "for two CAP skeletal finite sets",
-        [ IsSkeletalFiniteSet, IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets, IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s, t )
     local iota;
@@ -126,7 +126,7 @@ end );
 ##
 InstallMethod( Preimage,
         "for a CAP map of skeletal finite sets and a CAP skeletal finite set",
-        [ IsSkeletalFiniteSetMap, IsList ],
+        [ IsMorphismInCategoryOfSkeletalFinSets, IsList ],
         
   function ( phi, t )
     local S;
@@ -142,7 +142,7 @@ end );
 ##
 InstallMethod( ImageObject,
      "for a CAP map of skeletal finite sets and a CAP skeletal finite set",
-     [ IsSkeletalFiniteSetMap, IsSkeletalFiniteSet ],
+     [ IsMorphismInCategoryOfSkeletalFinSets, IsObjectInCategoryOfSkeletalFinSets ],
       function ( phi, s_ )
 
     return ImageObject( PreCompose( EmbeddingOfFinSets( s_, Source( phi ) ), phi ) );
@@ -152,7 +152,7 @@ end );
 ##
 InstallMethod( CallFuncList,
         "for a CAP map of skeletal finite sets and a list",
-    [ IsSkeletalFiniteSetMap, IsList ],
+    [ IsMorphismInCategoryOfSkeletalFinSets, IsList ],
         
   function ( phi, L )
     local x;
@@ -988,7 +988,7 @@ end );
 ##
 InstallMethod( String,
         "for a CAP skeletal finite set",
-        [ IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s )
     return Concatenation( "FinSet( SkeletalFinSets, ", String( Length( s ) ), " )" );
@@ -997,7 +997,7 @@ end );
 ##
 InstallMethod( String,
         "for a CAP map of skeletal finite sets",
-        [ IsSkeletalFiniteSetMap ],
+        [ IsMorphismInCategoryOfSkeletalFinSets ],
         
   function ( phi )
     return Concatenation( "MapOfFinSets( SkeletalFinSets, ", String( Source( phi ) ), ", ", String( AsList( phi ) ), ", ", String( Range( phi ) ), " )" );
@@ -1006,7 +1006,7 @@ end );
 ##
 InstallMethod( ViewString,
         "for a CAP skeletal finite set",
-        [ IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s )
     return Concatenation( "|", String( Length( s ) ), "|" );
@@ -1015,7 +1015,7 @@ end );
 ##
 InstallMethod( ViewString,
         "for a CAP map of skeletal finite sets",
-        [ IsSkeletalFiniteSetMap ],
+        [ IsMorphismInCategoryOfSkeletalFinSets ],
         
   function ( phi )
     local arrow;
@@ -1049,7 +1049,7 @@ end );
 ##
 InstallMethod( PrintString,
         "for a CAP skeletal finite set",
-        [ IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s )
     local l, string;
@@ -1073,7 +1073,7 @@ end );
 ##
 InstallMethod( PrintString,
         "for a CAP map of skeletal finite sets",
-        [ IsSkeletalFiniteSetMap ],
+        [ IsMorphismInCategoryOfSkeletalFinSets ],
         
   function ( phi )
     
@@ -1087,7 +1087,7 @@ end );
 ##
 InstallMethod( DisplayString,
         "for a CAP skeletal finite set",
-        [ IsSkeletalFiniteSet ],
+        [ IsObjectInCategoryOfSkeletalFinSets ],
         
   function ( s )
     
@@ -1098,7 +1098,7 @@ end );
 ##
 InstallMethod( DisplayString,
         "for a CAP map of skeletal finite sets",
-        [ IsSkeletalFiniteSetMap ],
+        [ IsMorphismInCategoryOfSkeletalFinSets ],
         
   function ( phi )
     
@@ -1116,3 +1116,6 @@ InstallOtherMethod( FinSet,
     return FinSet( SkeletalFinSets, n );
     
 end );
+
+DeclareSynonym( "IsSkeletalFiniteSet", IsObjectInCategoryOfSkeletalFinSets );
+DeclareSynonym( "IsSkeletalFiniteSetMap", IsMorphismInCategoryOfSkeletalFinSets );