Several category constructors now use FinQuiver instead of RightQuiver

* SimplicialCategoryTruncatedInDegree
* CategoryOfBouquetsEnrichedOver
* CategoryOfQuiversEnrichedOver

Algebroids/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "Algebroids",
 Subtitle := "Algebroids and bialgebroids as preadditive categories generated by enhanced quivers",
-Version := "2024.09-03",
+Version := "2024.09-04",
 Date := ~.Version{[ 1 .. 10 ]},
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
@@ -137,7 +137,7 @@ Dependencies := rec(
                    [ "CartesianCategories", ">= 2024.02-01" ],
                    [ "Toposes", ">= 2023.03-05" ],
                    [ "FinSetsForCAP", ">= 2024.02-02" ],
-                   [ "FpCategories", ">= 2024.09-04" ],
+                   [ "FpCategories", ">= 2024.09-06" ],
                    [ "QPA", ">= 2.0" ],
                    [ "MatricesForHomalg", ">= 2021.12-01" ],
                    [ "FreydCategoriesForCAP", ">= 2024.07-05" ],

Algebroids/doc/Doc.autodoc

@@ -9,9 +9,6 @@
 @Section A f.p. category
 @InsertChunk FpCategory
 
-@Section The full subcategory of the simplicial category truncated in degree 2
-@InsertChunk Delta2
-
 @Section Algebroids
 @InsertChunk Algebroid
 
@@ -103,5 +100,4 @@
 @InsertChunk PrecompileAdditiveClosureOfAlgebroid
 @InsertChunk PrecompileAdditiveClosureOfAlgebroidFromDataTables
 @InsertChunk PrecompileAdelmanCategoryOfAdditiveClosureOfAlgebroid
-@InsertChunk PrecompileCategoryFromNerveData
 @InsertChunk PrecompileCategoryFromDataTables

Algebroids/examples/CategoryFromDataTables.g

@@ -4,20 +4,20 @@
 LoadPackage( "Algebroids", false );
 #! true
 Delta1 := SimplicialCategoryTruncatedInDegree( 1 );
-#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
-#! / [ s*id = C0, t*id = C0 ]
+#! PathCategory( FinQuiver( "Delta(C0,C1)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1]" ) )
+#! / [ s⋅id = id(C0), t⋅id = id(C0) ]
 Size( Delta1 );
 #! 7
 mors := SetOfMorphisms( Delta1 );
-#! [ (C0)-[(C0)]->(C0), (C1)-[(id)]->(C0), (C0)-[(s)]->(C1), (C0)-[(t)]->(C1),
-#!   (C1)-[(C1)]->(C1), (C1)-[(id*s)]->(C1), (C1)-[(id*t)]->(C1) ]
+#! [ [id(C0)]:(C0) -≻ (C0), [id]:(C1) -≻ (C0), [s]:(C0) -≻ (C1), [t]:(C0) -≻ (C1),
+#!   [id(C1)]:(C1) -≻ (C1), [id⋅s]:(C1) -≻ (C1), [id⋅t]:(C1) -≻ (C1) ]
 List( mors, DecompositionOfMorphismInCategory );
-#! [ [  ], [ (C1)-[(id)]->(C0) ], [ (C0)-[(s)]->(C1) ], [ (C0)-[(t)]->(C1) ],
-#!   [  ], [ (C1)-[(id)]->(C0), (C0)-[(s)]->(C1) ],
-#!   [ (C1)-[(id)]->(C0), (C0)-[(t)]->(C1) ] ]
+#! [ [  ], [ [id]:(C1) -≻ (C0) ], [ [s]:(C0) -≻ (C1) ], [ [t]:(C0) -≻ (C1) ],
+#!   [  ], [ [id]:(C1) -≻ (C0), [s]:(C0) -≻ (C1) ],
+#!   [ [id]:(C1) -≻ (C0), [t]:(C0) -≻ (C1) ] ]
 C := CategoryFromDataTables( Delta1 );
-#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
-#! / [ s*id = C0, t*id = C0 ]
+#! PathCategory( FinQuiver( "Delta(C0,C1)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1]" ) )
+#! / [ s⋅id = id(C0), t⋅id = id(C0) ]
 Size( C );
 #! 7
 morsC := SetOfMorphisms( C );
@@ -35,8 +35,8 @@ SetOfGeneratingMorphisms( C );
 #! [ (C1)-[(id)]->(C0), (C0)-[(s)]->(C1), (C0)-[(t)]->(C1) ]
 Display( C );
 #! A CAP category with name
-#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
-#! / [ s*id = C0, t*id = C0 ]:
+#! PathCategory( FinQuiver( "Delta(C0,C1)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1]" ) )
+#! / [ s⋅id = id(C0), t⋅id = id(C0) ]:
 #! 
 #! 19 primitive operations were used to derive 55 operations for this category
 #! which algorithmically
@@ -161,8 +161,8 @@ List( mors, DecompositionOfMorphismInCategory );
 #!   [ (C1)-[(id)]->(C0), (C0)-[(t)]->(C1) ] ]
 C_op := OppositeCategoryFromDataTables( C );
 #! Opposite(
-#! FreeCategory( RightQuiver( "Delta(C0,C1)[id:C1->C0,s:C0->C1,t:C0->C1]" ) )
-#! / [ s*id = C0, t*id = C0 ] )
+#! PathCategory( FinQuiver( "Delta(C0,C1)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1]" ) )
+#! / [ s⋅id = id(C0), t⋅id = id(C0) ] )
 IsIdenticalObj( OppositeCategoryFromDataTables( C_op ), C );
 #! true
 IndicesOfGeneratingMorphisms( C_op );

Algebroids/gap/Algebroids.gd

@@ -463,20 +463,6 @@ DeclareOperation( "CapFunctor",
 DeclareOperation( "CapFunctor",
         [ IsAlgebroid, IsCapCategoryObject ] );
 
-#! @Description
-#!  Construct, using the record (or list) of images <A>eta</A>, a natural transformation
-#!  from the functor <A>F</A> to the parallel functor <A>G</A>.
-#! @Arguments eta, F, G
-#! @Returns a &CAP; natural transformation
-#! @Group NaturalTransformation
-DeclareOperation( "NaturalTransformation",
-        [ IsRecord, IsCapFunctor, IsCapFunctor ] );
-
-#! @Arguments F, eta, G
-#! @Group NaturalTransformation
-DeclareOperation( "NaturalTransformation",
-        [ IsCapFunctor, IsList, IsCapFunctor ] );
-
 #! @Description
 #!  The constructor of objects in an algebroid <A>A</A> given a vertex <A>V</A>
 #!  in the underlying quiver.

Algebroids/gap/Algebroids.gi

@@ -2161,38 +2161,6 @@ InstallMethod( IsCommutative,
     return true;
 end );
 
-##
-InstallMethod( NaturalTransformation,
-        "for a list and two CAP functors",
-        [ IsCapFunctor, IsList, IsCapFunctor ],
-
-  function( F, images, G )
-    local eta, vertices;
-
-    eta := NaturalTransformation( Concatenation( "Natural transformation from ", Name( F ), " -> ", Name( G ) ), F, G );
-
-    eta!.ValuesOnAllObjects := images;
-
-    vertices := Vertices( QuiverOfAlgebra( UnderlyingQuiverAlgebra( AsCapCategory( Source( F ) ) ) ) );
-
-    AddNaturalTransformationFunction( eta,
-      function( source, obj, range )
-        local pos;
-
-        pos := SafePosition( vertices, UnderlyingVertex( obj ) );
-
-        if not IsInt( pos ) then
-            Error( "vertex UnderlyingVertex( obj ) = ", UnderlyingVertex( obj ), " not found in the list ", vertices, " of vertices\n" );
-        fi;
-
-        return images[pos];
-
-    end );
-
-    return eta;
-
-end );
-
 ##
 InstallMethod( NaturalTransformation,
         "for a record and two CAP functors",

Algebroids/gap/CategoryFromDataTables.gd

@@ -173,6 +173,14 @@ DeclareAttribute( "CategoryFromDataTables",
 DeclareAttribute( "CategoryFromDataTables",
         IsFpCategory );
 
+#! @Arguments C
+DeclareAttribute( "CategoryFromDataTables",
+        IsPathCategory );
+
+#! @Arguments C
+DeclareAttribute( "CategoryFromDataTables",
+        IsQuotientOfPathCategory );
+
 #! @Arguments C
 DeclareAttribute( "CategoryFromDataTables",
         IsCategoryFromNerveData );

Algebroids/gap/CategoryFromDataTables.gi

@@ -356,6 +356,45 @@ InstallMethod( CategoryFromDataTables,
 
 end );
 
+##
+InstallMethod( CategoryFromDataTables,
+        "for a path category",
+        [ IsPathCategory ],
+
+  function( C )
+
+    return CategoryFromDataTables(
+                   rec( name := Name( C ),
+                        range_of_HomStructure := RangeCategoryOfHomomorphismStructure( C ),
+                        data_tables := DataTablesOfCategory( C ),
+                        indices_of_generating_morphisms := IndicesOfGeneratingMorphismsFromHomStructure( C ),
+                        decomposition_of_all_morphisms := DecompositionIndicesOfAllMorphismsFromHomStructure( C ),
+                        relations := RelationsAmongGeneratingMorphisms( C ),
+                        labels := [ List( SetOfObjects( C ), ObjectLabel ), List( SetOfGeneratingMorphisms( C ), MorphismLabel ) ],
+                        properties := ListKnownCategoricalProperties( C ) ) );
+
+end );
+
+##
+InstallMethod( CategoryFromDataTables,
+        "for a quotient of a path category",
+        [ IsQuotientOfPathCategory ],
+
+  function( C )
+
+    return CategoryFromDataTables(
+                   rec( name := Name( C ),
+                        range_of_HomStructure := RangeCategoryOfHomomorphismStructure( C ),
+                        data_tables := DataTablesOfCategory( C ),
+                        indices_of_generating_morphisms := IndicesOfGeneratingMorphismsFromHomStructure( C ),
+                        decomposition_of_all_morphisms := DecompositionIndicesOfAllMorphismsFromHomStructure( C ),
+                        relations := RelationsAmongGeneratingMorphisms( C ),
+                        labels := [ List( SetOfObjects( C ), o -> ObjectLabel( UnderlyingCell( o ) ) ),
+                                List( SetOfGeneratingMorphisms( C ), m -> MorphismLabel( CanonicalRepresentative( m ) ) ) ],
+                        properties := ListKnownCategoricalProperties( C ) ) );
+
+end );
+
 ##
 InstallMethod( CategoryFromDataTables,
         "for a category from nerve data",
@@ -499,6 +538,24 @@ InstallMethod( \.,
 
 end );
 
+##
+InstallOtherMethod( CategoryFromNerveData,
+        "for a category from data tables",
+        [ IsCategoryFromDataTables ],
+
+  function( C )
+
+    return CategoryFromNerveData(
+                   rec( name := Name( C ),
+                        nerve_data := NerveTruncatedInDegree2Data( C ),
+                        indices_of_generating_morphisms := IndicesOfGeneratingMorphismsFromHomStructure( C ),
+                        decomposition_of_all_morphisms := DecompositionIndicesOfAllMorphisms( C ),
+                        relations := RelationsAmongGeneratingMorphisms( C ),
+                        labels := C!.labels,
+                        properties := ListKnownCategoricalProperties( C ) ) );
+
+end );
+
 ##
 InstallMethod( OppositeCategoryFromDataTables,
         "for a category from data tables",