Move QuiverRows to Algebroids

FreydCategoriesForCAP/PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "FreydCategoriesForCAP",
 Subtitle := "Freyd categories - Formal (co)kernels for additive categories",
-Version := "2022.12-03",
+Version := "2022.12-04",
 Date := Concatenation( "01/", ~.Version{[ 6, 7 ]}, "/", ~.Version{[ 1 .. 4 ]} ),
 License := "GPL-2.0-or-later",
 
@@ -94,7 +94,6 @@ Dependencies := rec(
                            [ "GeneralizedMorphismsForCAP", ">= 2018.06.15" ]
                          ],
   SuggestedOtherPackages := [
-    [ "QPA", ">= 2.0" ],
     [ "FinSetsForCAP", ">= 2022.05-01" ]
    ],
   ExternalConditions := [ ],

FreydCategoriesForCAP/examples/AdelmanCategoryBasics.g

@@ -59,67 +59,6 @@ IsCongruentForMorphisms( KernelLift( m, KernelEmbedding( m ) ), IdentityMorphism
 #! true
 #! @EndExample
 
-#! @Section Adelman category basics for for additive closure of algebroids
-
-#! @Example
-#! #@if IsPackageMarkedForLoading( "QPA", ">= 2.0" )
-LoadPackage( "Algebroids", false );
-#! true
-quiver := RightQuiver( "Q(9)[a:1->2,b:2->3,c:1->4,d:2->5,e:3->6,f:4->5,g:5->6,h:4->7,i:5->8,j:6->9,k:7->8,l:8->9,m:2->7,n:3->8]" );;
-kQ := PathAlgebra( HomalgFieldOfRationals(), quiver );;
-Aoid := Algebroid( kQ, [ kQ.ad - kQ.cf, 
-                         kQ.dg - kQ.be, 
-                         kQ.("fi") - kQ.hk,
-                         kQ.gj - kQ.il,
-                         kQ.mk + kQ.bn - kQ.di ] );;
-mm := SetOfGeneratingMorphisms( Aoid );;
-CapCategorySwitchLogicOff( Aoid );;
-Acat := AdditiveClosure( Aoid );;
-a := AsAdditiveClosureMorphism( mm[1] );;
-b := AsAdditiveClosureMorphism( mm[2] );;
-c := AsAdditiveClosureMorphism( mm[3] );;
-d := AsAdditiveClosureMorphism( mm[4] );;
-e := AsAdditiveClosureMorphism( mm[5] );;
-f := AsAdditiveClosureMorphism( mm[6] );;
-g := AsAdditiveClosureMorphism( mm[7] );;
-h := AsAdditiveClosureMorphism( mm[8] );;
-i := AsAdditiveClosureMorphism( mm[9] );;
-j := AsAdditiveClosureMorphism( mm[10] );;
-k := AsAdditiveClosureMorphism( mm[11] );;
-l := AsAdditiveClosureMorphism( mm[12] );;
-m := AsAdditiveClosureMorphism( mm[13] );;
-n := AsAdditiveClosureMorphism( mm[14] );;
-Adel := AdelmanCategory( Acat );;
-A := AdelmanCategoryObject( a, b );;
-B := AdelmanCategoryObject( f, g );;
-alpha := AdelmanCategoryMorphism( A, d, B );;
-IsWellDefined( alpha );
-#! true
-IsWellDefined( KernelEmbedding( alpha ) );
-#! true
-IsWellDefined( CokernelProjection( alpha ) );
-#! true
-T := AdelmanCategoryObject( k, l );;
-tau := AdelmanCategoryMorphism( B, i, T );;
-IsZeroForMorphisms( PreCompose( alpha, tau ) );
-#! true
-colift := CokernelColift( alpha, tau );;
-IsWellDefined( colift );
-#! true
-IsCongruentForMorphisms( PreCompose( CokernelProjection( alpha ), colift ), tau );
-#! true
-lift := KernelLift( tau, alpha );;
-IsWellDefined( lift );
-#! true
-IsCongruentForMorphisms( PreCompose( lift, KernelEmbedding( tau ) ), alpha );
-#! true
-IsCongruentForMorphisms( ColiftAlongEpimorphism( CokernelProjection( alpha ), tau ), colift );
-#! true
-IsCongruentForMorphisms( LiftAlongMonomorphism( KernelEmbedding( tau ), alpha ), lift );
-#! true
-#! #@fi
-#! @EndExample
-
 #! @Section Adelman category basics for category of columns
 
 #! @Example

FreydCategoriesForCAP/examples/Basics.gi

@@ -196,63 +196,6 @@ InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism( Sourc
 #! true
 #! @EndExample
 
-
-#! @Section Basics of additive closure
-
-#! @Example
-## Algebroid
-#! #@if IsPackageMarkedForLoading( "QPA", ">= 2.0" )
-LoadPackage( "Algebroids", false );
-#! true
-snake_quiver := RightQuiver( "Q(6)[a:1->2,b:2->3,c:1->4,d:2->5,e:3->6,f:4->5,g:5->6]" );;
-kQ := PathAlgebra( HomalgFieldOfRationalsInSingular(), snake_quiver );;
-A := kQ / [ kQ.ad - kQ.cf, kQ.dg - kQ.be, kQ.ab, kQ.fg ];;
-Aoid := Algebroid( kQ, [ kQ.ad - kQ.cf, kQ.dg - kQ.be, kQ.ab, kQ.fg ] );;
-s := SetOfObjects( Aoid );;
-m := SetOfGeneratingMorphisms( Aoid );;
-interpretation := InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure( -m[3] );;
-InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism( Source( m[3] ), Range( m[3] ), interpretation );;
-
-## additive closure
-add := AdditiveClosure( Aoid );;
-obj1 := AdditiveClosureObject( [ s[1], s[2] ], add );;
-mor := AdditiveClosureMorphism( obj1, [ [ IdentityMorphism( s[1] ), ZeroMorphism( s[1], s[2] ) ], [ ZeroMorphism( s[2], s[1] ), -IdentityMorphism( s[2] ) ] ], obj1 );;
-IsWellDefined( mor );;
-IsCongruentForMorphisms( PreCompose( mor, mor ), IdentityMorphism( obj1 ) );;
-obj2 := AdditiveClosureObject( [ s[3], s[3] ], add );;
-id := IdentityMorphism( obj2 );;
-objs1:= AdditiveClosureObject( [ s[1] ], add );;
-objs2:= AdditiveClosureObject( [ s[2] ], add );;
-ids1 := IdentityMorphism( objs1 );;
-ids2 := IdentityMorphism( objs2 );;
-HomomorphismStructureOnMorphisms( DirectSumFunctorial( [ ids1, ids2 ] ), ids1 );;
-
-interpretation := InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure( mor );;
-IsCongruentForMorphisms(
-  InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism( Source( mor ), Range( mor ), interpretation ),
-  mor );;
-
-a := AsAdditiveClosureMorphism( m[1] );;
-b := AsAdditiveClosureMorphism( m[2] );;
-c := AsAdditiveClosureMorphism( m[3] );;
-d := AsAdditiveClosureMorphism( m[4] );;
-e := AsAdditiveClosureMorphism( m[5] );;
-f := AsAdditiveClosureMorphism( m[6] );;
-g := AsAdditiveClosureMorphism( m[7] );;
-
-l := Lift( PreCompose( a, d ), f );;
-IsCongruentForMorphisms( PreCompose( l, f ), PreCompose( a, d ) );
-#! true
-l := Colift( c, PreCompose( a, d ) );;
-IsCongruentForMorphisms( PreCompose( c, l ), PreCompose( a, d ) );
-#! true
-#! #@fi
-#! @EndExample
-
-
-
-
-
 #! @Section Basics based on category of columns
 
 #! @Example