d&i CategoryFromNerveData/DataTables using IndicesOfGeneratingMorphisms

and used it to simplify example files
* CategoryFromNerveData.g
* CategoryFromDataTables.g

Author: mohamed-barakat

PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "Algebroids",
 Subtitle := "Algebroids and bialgebroids as preadditive categories generated by enhanced quivers",
-Version := "2022.12-28",
+Version := "2022.12-29",
 
 Date := ~.Version{[ 1 .. 10 ]},
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),

examples/CategoryFromDataTables.g

@@ -6,12 +6,7 @@ LoadPackage( "Algebroids" );
 Delta1 := SimplicialCategoryTruncatedInDegree( 1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
-C := CategoryFromDataTables( Name( Delta1 ),
-             RangeCategoryOfHomomorphismStructure( Delta1 ),
-             DataTablesOfCategory( Delta1 ),
-             IndicesOfGeneratingMorphisms( Delta1 ),
-             [ [ "C0", "C1" ],
-               [ "id", "s", "t" ] ] );
+C := CategoryFromDataTables( Delta1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
 NerveTruncatedInDegree2Data( Delta1 ) = NerveTruncatedInDegree2Data( C );

examples/CategoryFromNerveData.g

@@ -9,11 +9,7 @@ Delta1 := SimplicialCategoryTruncatedInDegree( 1 );
 N1 := NerveTruncatedInDegree2Data( Delta1 );;
 N1[1];
 #! [ |2|, |7|, |26| ]
-C := CategoryFromNerveData( Name( Delta1 ),
-             N1,
-             IndicesOfGeneratingMorphisms( Delta1 ),
-             [ [ "C0", "C1" ],
-               [ "id", "s", "t" ] ] );
+C := CategoryFromNerveData( Delta1 );
 #! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
 #! / [ s*id = C0, t*id = C0 ]
 NerveTruncatedInDegree2Data( C ) = N1;

gap/CategoryFromDataTables.gd

@@ -182,13 +182,17 @@ DeclareAttribute( "OppositeCategoryFromDataTables",
 ####################################
 
 #! @Description
-#!  Construct a <A>V</A>-enriched category with name <A>str</A> from the given <A>data_tables</A>.
+#!  Construct a <A>V</A>-enriched category with name <A>str</A> from the given <A>data_tables</A> (of a f.p. category <A>C</A>).
 #! @Arguments str, V, data_tables, indices_of_generating_morphisms, labels
 #! @Returns a &CAP; category
 DeclareOperation( "CategoryFromDataTables",
         [ IsString, IsCapCategory, IsList, IsList, IsList ] );
 #! @InsertChunk CategoryFromDataTables
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromDataTables",
+        IsFpCategory );
+
 #! @Description
 #!  Construct the <A>o</A>-th object in the category <A>C</A> created from data tables.
 #! @Arguments C, o

gap/CategoryFromDataTables.gi

@@ -258,6 +258,22 @@ InstallMethod( CategoryFromDataTables,
 
 end );
 
+##
+InstallMethod( CategoryFromDataTables,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    
+    return CategoryFromDataTables( Name( C ),
+                   RangeCategoryOfHomomorphismStructure( C ),
+                   DataTablesOfCategory( C ),
+                   IndicesOfGeneratingMorphisms( C ),
+                   [ List( SetOfObjects( C ), Label ),
+                     List( SetOfGeneratingMorphisms( C ), Label ) ] );
+    
+end );
+
 ##
 InstallMethodForCompilerForCAP( CreateObject,
         "for a category from data tables and an integer",

gap/CategoryFromNerveData.gd

@@ -167,13 +167,17 @@ DeclareAttribute( "OppositeCategoryFromNerveData",
 ####################################
 
 #! @Description
-#!  Construct a category with name <A>str</A> from the given <A>nerve_data</A>.
+#!  Construct a category with name <A>str</A> from the given <A>nerve_data</A> (of a f.p. category <A>C</A>).
 #! @Arguments str, nerve_data, indices_of_generating_morphisms, labels
 #! @Returns a &CAP; category
 DeclareOperation( "CategoryFromNerveData",
         [ IsString, IsList, IsList, IsList ] );
 #! @InsertChunk CategoryFromNerveData
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromNerveData",
+        IsFpCategory );
+
 #! @Description
 #!  Construct the <A>o</A>-th object in the category <A>C</A> created from nerve data.
 #! @Arguments C, o

gap/CategoryFromNerveData.gi

@@ -476,6 +476,21 @@ InstallMethod( CategoryFromNerveData,
 
 end );
 
+##
+InstallMethod( CategoryFromNerveData,
+        "for a f.p. category",
+        [ IsFpCategory ],
+        
+  function( C )
+    
+    return CategoryFromNerveData( Name( C ),
+                   NerveTruncatedInDegree2Data( C ),
+                   IndicesOfGeneratingMorphisms( C ),
+                   [ List( SetOfObjects( C ), Label ),
+                     List( SetOfGeneratingMorphisms( C ), Label ) ] );
+    
+end );
+
 ##
 InstallMethod( CreateObject,
         "for a category from nerve data and an integer",