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2 Examples and Tests
 2.1 Basics

2 Examples and Tests

2.1 Basics

gap> vecspaces := CreateCapCategory( "VectorSpaces" );;
gap> ReadPackage( "MonoidalCategories", "examples/VectorSpacesMonoidalCategory.gi" );;
gap> z := ZeroObject( vecspaces );;
gap> a := QVectorSpace( 1 );;
gap> b := QVectorSpace( 2 );;
gap> c := QVectorSpace( 3 );;
gap> alpha := VectorSpaceMorphism( a, [ [ 1, 0 ] ], b );;
gap> beta := VectorSpaceMorphism( b, [ [ 1, 0, 0 ], [ 0, 1, 0 ] ], c );;
gap> gamma := VectorSpaceMorphism( c, [ [ 0, 1, 1 ], [ 1, 0, 1 ], [ 1, 1, 0 ] ], c );;
gap> IsCongruentForMorphisms( TensorProductOnMorphisms( alpha, beta ), TensorProductOnMorphisms( beta, alpha ) );
false
gap> IsOne( AssociatorRightToLeft( a, b, c ) );
true
gap> IsCongruentForMorphisms( gamma, LambdaElimination( c, c, LambdaIntroduction( gamma ) ) );
true
gap> IsZero( TraceMap( gamma ) );
true
gap> IsCongruentForMorphisms( RankMorphism( DirectSum( a, b ) ), RankMorphism( c ) );
true
gap> IsOne( Braiding( b, c ) );
false
gap> IsOne( PreCompose( Braiding( b, c ), Braiding( c, b ) ) );
true
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