AdditiveClosureOfObjectFiniteCategory

AdditiveClosuresForCAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "AdditiveClosuresForCAP",
 Subtitle := "Additive closures for pre-additive categories",
-Version := "2026.07-03",
+Version := "2026.08-01",
 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",
 

AdditiveClosuresForCAP/doc/Doc.autodoc

@@ -15,11 +15,23 @@
 @Section GAP Categories
 
 @Chapter Reinterpret a linear category over a commutative semiring with free f.g. external Homs
-@Section Constructors
+
+@Chapter Example on additive closure
+
+@Chapter Additive closure of an object finite category
+@ChapterLabel AdditiveClosureObjectFinite
+
+@InsertChunk AddClosureObjFinIntroduction
+@InsertChunk AddClosureObjFinConstruction
 @Section Attributes
+@Section Constructors
+@Section Operations
+@Section Operators
 @Section GAP Categories
+@Section Examples
 
-@Chapter Example on additive closure
+@Subsection Test Monoidal
+@InsertChunk AddClosureObjFinKronecker
 
 @Chapter Category of rows
 @Section Constructors

AdditiveClosuresForCAP/examples/AdditiveClosureOfObjectFiniteCategory_Kronecker.g

@@ -0,0 +1,23 @@
+#! @BeginChunk AddClosureObjFinKronecker
+
+#! @Example
+LoadPackage( "AdditiveClosuresForCAP", false );
+#! true
+Q := HomalgFieldOfRationals();;
+R := RingAsCategory( Q );;
+A := AdditiveClosureOfObjectFiniteCategory( R );;
+u := TensorUnit( A );;
+mor1 := [ [ 1 / R, 2 / R ] ] / A;;
+mor2 := [ [ 3 / R, 4 / R ] ] / A;;
+T := TensorProduct( mor1, mor2 );;
+Display( T );
+#! A 1 x 4 matrix with entries in RingAsCategory( Q )
+#! 
+#! [1,1]: <3>
+#! [1,2]: <4>
+#! [1,3]: <6>
+#! [1,4]: <8>
+Display( Range( T ) );
+#! A formal direct sum consisting of 4 objects:
+#! 4 times: *
+#! @EndExample

AdditiveClosuresForCAP/examples/AdditiveClosureOfObjectFiniteCategory_constructors.g

@@ -0,0 +1,47 @@
+#! @BeginChunk AddClosureObjFinConstruction
+
+#! @Example
+LoadPackage( "LinearClosuresForCAP", false );
+#! true
+D := FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] );;
+Q := HomalgFieldOfRationals( );;
+L := LinearClosure( Q, D );;
+A := AdditiveClosureOfObjectFiniteCategory( L );;
+source := AdditiveClosureObject( A, [ 3, [ 2, 1, 0, 0 ] ] );;
+source = [ D[1] / L, D[2] / L, D[1] / L ] / A;
+#! true
+Display( source );
+#! A formal direct sum consisting of 3 objects:
+#! 
+#! 2 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 1 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 0 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 0 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+target := AdditiveClosureObject( A, [ 2, [ 0, 1, 1, 0 ] ] );;
+Display( target );
+#! A formal direct sum consisting of 2 objects:
+#! 
+#! 0 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 1 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 1 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! 0 times: LinearClosureObject(<An object in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+id_2 := IdentityMorphism( D[2] / L );;
+zero_12 := ZeroMorphism( L, D[1] / L, D[2] / L );;
+zero_13 := ZeroMorphism( L, D[1] / L, D[3] / L );;
+zero_23 := ZeroMorphism( L, D[2] / L, D[3] / L );;
+matrix := [ [ zero_12, zero_13 ], [ zero_12, zero_13 ], [ id_2, zero_23] ];;
+m := AdditiveClosureMorphism( A, source, matrix, target );;
+m = matrix / A;
+#! true
+Display( m );
+#! A 3 x 2 matrix with entries in LinearClosure( FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] ) )
+#! 
+#! [1,1]: 0
+#! [1,2]: 0
+#! [2,1]: 0
+#! [2,2]: 0
+#! [3,1]: (1*<An identity morphism in FiniteSkeletalDiscreteCategory( [ 1 .. 4 ] )>)
+#! [3,2]: 0
+#! @EndExample
+#! @EndChunk
+

AdditiveClosuresForCAP/examples/CategoryOfRows.g

@@ -21,6 +21,13 @@ obj2 := CategoryOfRowsObject( 8, rows );
 #! @Section Constructors of morphisms
 #####################################
 
+s := CategoryOfRowsObject( 2, rows );;
+t := CategoryOfRowsObject( 0, rows );;
+mor := CategoryOfRowsMorphism( s, HomalgMatrix( [ [],[] ], 2, 0, S ), t );;
+IsWellDefined( mor );
+
+mor := CategoryOfRowsMorphism( s, HomalgMatrix( [ ], 2, 0, S ), t );;
+
 #! @Example
 obj3 := CategoryOfRowsObject( 1, rows );
 #! <A row module over Z of rank 1>