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# LinearAlgebraForCAP, single 13
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("linearalgebraforcap13.tst");
# doc/_Chapter_Examples_and_Tests.xml:640-705
gap> LoadPackage( "LinearAlgebraForCAP", ">= 2024.01-04", false );
true
gap> QQ := HomalgFieldOfRationals();;
gap> vec := MatrixCategory( QQ );;
gap> op := Opposite( vec );;
gap> Perform( ListKnownCategoricalProperties( op ), Display );
IsAbCategory
IsAbelianCategory
IsAbelianCategoryWithEnoughInjectives
IsAbelianCategoryWithEnoughProjectives
IsAdditiveCategory
IsAdditiveMonoidalCategory
IsBraidedMonoidalCategory
IsCategoryWithCoequalizers
IsCategoryWithCokernels
IsCategoryWithEqualizers
IsCategoryWithInitialObject
IsCategoryWithKernels
IsCategoryWithTerminalObject
IsCategoryWithZeroObject
IsClosedMonoidalCategory
IsCoclosedMonoidalCategory
IsEnrichedOverCommutativeRegularSemigroup
IsEquippedWithHomomorphismStructure
IsLinearCategoryOverCommutativeRing
IsLinearCategoryOverCommutativeRingWithFinitelyGeneratedFreeExternalHoms
IsMonoidalCategory
IsPreAbelianCategory
IsRigidSymmetricClosedMonoidalCategory
IsRigidSymmetricCoclosedMonoidalCategory
IsSkeletalCategory
IsStrictMonoidalCategory
IsSymmetricClosedMonoidalCategory
IsSymmetricCoclosedMonoidalCategory
IsSymmetricMonoidalCategory
gap> V1 := Opposite( TensorUnit( vec ) );;
gap> V2 := DirectSum( V1, V1 );;
gap> V3 := DirectSum( V1, V2 );;
gap> V4 := DirectSum( V1, V3 );;
gap> V5 := DirectSum( V1, V4 );;
gap> IsWellDefined( MorphismBetweenDirectSums( op, [ ], [ ], [ V1 ] ) );
true
gap> IsWellDefined( MorphismBetweenDirectSums( op, [ V1 ], [ [ ] ], [ ] ) );
true
gap> alpha13 := InjectionOfCofactorOfDirectSum( [ V1, V2 ], 1 );;
gap> alpha14 := InjectionOfCofactorOfDirectSum( [ V1, V2, V1 ], 3 );;
gap> alpha15 := InjectionOfCofactorOfDirectSum( [ V2, V1, V2 ], 2 );;
gap> alpha23 := InjectionOfCofactorOfDirectSum( [ V2, V1 ], 1 );;
gap> alpha24 := InjectionOfCofactorOfDirectSum( [ V1, V2, V1 ], 2 );;
gap> alpha25 := InjectionOfCofactorOfDirectSum( [ V2, V2, V1 ], 1 );;
gap> mat := [
> [ alpha13, alpha14, alpha15 ],
> [ alpha23, alpha24, alpha25 ]
> ];;
gap> mor := MorphismBetweenDirectSums( mat );;
gap> IsWellDefined( mor );
true
gap> IsWellDefined( Opposite( mor ) );
true
gap> IsCongruentForMorphisms(
> UniversalMorphismFromImage( mor, [ CoastrictionToImage( mor ), ImageEmbedding( mor ) ] ),
> IdentityMorphism( ImageObject( mor ) )
> );
true
#
gap> STOP_TEST("linearalgebraforcap13.tst", 1);
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