d&i CategoryFromDataTables for IsCategoryFromNerveData

and used it to simplify OppositeCategoryFromDataTables

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 := "2022.12-32",
+Version := "2022.12-33",
 
 Date := ~.Version{[ 1 .. 10 ]},
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),

gap/CategoryFromDataTables.gd

@@ -206,7 +206,8 @@ DeclareAttribute( "OppositeCategoryFromDataTables",
 ####################################
 
 #! @Description
-#!  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>).
+#!  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> or a category <A>C</A> created from nerve data).
 #! @Arguments str, V, data_tables, indices_of_generating_morphisms, relations, labels
 #! @Returns a &CAP; category
 DeclareOperation( "CategoryFromDataTables",
@@ -217,6 +218,10 @@ DeclareOperation( "CategoryFromDataTables",
 DeclareAttribute( "CategoryFromDataTables",
         IsFpCategory );
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromDataTables",
+        IsCategoryFromNerveData );
+
 #! @Description
 #!  Construct the <A>o</A>-th object in the category <A>C</A> created from data tables.
 #! @Arguments C, o

gap/CategoryFromDataTables.gi

@@ -277,6 +277,22 @@ InstallMethod( CategoryFromDataTables,
 
 end );
 
+##
+InstallMethod( CategoryFromDataTables,
+        "for a category from nerve data",
+        [ IsCategoryFromNerveData ],
+        
+  function( C )
+    
+    return CategoryFromDataTables( Name( C ),
+                   RangeCategoryOfHomomorphismStructure( C ),
+                   DataTablesOfCategory( C ),
+                   IndicesOfGeneratingMorphisms( C ),
+                   RelationsAmongGeneratingMorphisms( C ),
+                   C!.labels );
+    
+end );
+
 ##
 InstallMethod( Size,
         "for a category from data tables",
@@ -458,13 +474,7 @@ InstallMethod( OppositeCategoryFromDataTables,
 
     Cop := OppositeCategoryFromNerveData( C_from_nerve );
 
-    C_op := CategoryFromDataTables(
-                    Name( Cop ),
-                    RangeCategoryOfHomomorphismStructure( Cop ),
-                    DataTablesOfCategory( Cop ),
-                    IndicesOfGeneratingMorphisms( Cop ),
-                    RelationsAmongGeneratingMorphisms( Cop ),
-                    Cop!.labels );
+    C_op := CategoryFromDataTables( Cop );
 
     SetOppositeCategoryFromDataTables( C_op, C );