  
  [1X2 [33X[0;0YExamples and Tests[133X[101X
  
  
  [1X2.1 [33X[0;0YBasics[133X[101X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xvecspaces := CreateCapCategory( "VectorSpaces" );;[127X[104X
    [4X[25Xgap>[125X [27XReadPackage( "MonoidalCategories", "examples/VectorSpacesMonoidalCategory.gi" );;[127X[104X
    [4X[25Xgap>[125X [27Xz := ZeroObject( vecspaces );;[127X[104X
    [4X[25Xgap>[125X [27Xa := QVectorSpace( 1 );;[127X[104X
    [4X[25Xgap>[125X [27Xb := QVectorSpace( 2 );;[127X[104X
    [4X[25Xgap>[125X [27Xc := QVectorSpace( 3 );;[127X[104X
    [4X[25Xgap>[125X [27Xalpha := VectorSpaceMorphism( a, [ [ 1, 0 ] ], b );;[127X[104X
    [4X[25Xgap>[125X [27Xbeta := VectorSpaceMorphism( b, [ [ 1, 0, 0 ], [ 0, 1, 0 ] ], c );;[127X[104X
    [4X[25Xgap>[125X [27Xgamma := VectorSpaceMorphism( c, [ [ 0, 1, 1 ], [ 1, 0, 1 ], [ 1, 1, 0 ] ], c );;[127X[104X
    [4X[25Xgap>[125X [27XIsCongruentForMorphisms( TensorProductOnMorphisms( alpha, beta ), TensorProductOnMorphisms( beta, alpha ) );[127X[104X
    [4X[28Xfalse[128X[104X
    [4X[25Xgap>[125X [27XIsOne( AssociatorRightToLeft( a, b, c ) );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XIsCongruentForMorphisms( gamma, LambdaElimination( c, c, LambdaIntroduction( gamma ) ) );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XIsZero( TraceMap( gamma ) );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XIsCongruentForMorphisms( RankMorphism( DirectSum( a, b ) ), RankMorphism( c ) );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XIsOne( Braiding( b, c ) );[127X[104X
    [4X[28Xfalse[128X[104X
    [4X[25Xgap>[125X [27XIsOne( PreCompose( Braiding( b, c ), Braiding( c, b ) ) );[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
