GAP (MonoidalCategories) - Chapter 2: Examples and Tests

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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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