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Merge pull request #1689 from damian-delafuente/MonAdd
Added monoidal structure to AdditiveClosure
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,33 @@ | ||
| #! @Chapter Examples and Tests | ||
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| #! @Section Monoidal structure of AdditiveClosure | ||
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| #! @Example | ||
| LoadPackage( "FreydCategoriesForCAP", false ); | ||
| #! true | ||
| Q := HomalgFieldOfRationals(); | ||
| #! Q | ||
| R := RingAsCategory( Q ); | ||
| #! RingAsCategory( Q ) | ||
| A := AdditiveClosure( R ); | ||
| #! AdditiveClosure( RingAsCategory( Q ) ) | ||
| u := TensorUnit( A ); | ||
| #! <An object in AdditiveClosure( RingAsCategory( Q ) ) | ||
| #! defined by 1 underlying objects> | ||
| mor1 := [ [ 1 / R, 2 / R ] ] / A; | ||
| #! <A morphism in AdditiveClosure( RingAsCategory( Q ) ) | ||
| #! defined by a 1 x 2 matrix of underlying morphisms> | ||
| mor2 := [ [ 3 / R, 4 / R ] ] / A; | ||
| #! <A morphism in AdditiveClosure( RingAsCategory( Q ) ) | ||
| #! defined by a 1 x 2 matrix of underlying morphisms> | ||
| T := TensorProduct( mor1, mor2 ); | ||
| #! <A morphism in AdditiveClosure( RingAsCategory( Q ) ) | ||
| #! defined by a 1 x 4 matrix of underlying morphisms> | ||
| Display( T ); | ||
| #! A 1 x 4 matrix with entries in RingAsCategory( Q ) | ||
| #! | ||
| #! [1,1]: <3> | ||
| #! [1,2]: <4> | ||
| #! [1,3]: <6> | ||
| #! [1,4]: <8> | ||
| #! @EndExample |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,86 @@ | ||
| #! @Chapter Examples and Tests | ||
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| #! @Section Monoidal structure of AdditiveClosure | ||
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| #! @Example | ||
| LoadPackage( "FreydCategoriesForCAP", false ); | ||
| #! true | ||
| T := TerminalCategoryWithMultipleObjects( ); | ||
| #! TerminalCategoryWithMultipleObjects( ) | ||
| A := "A" / T; | ||
| #! <A zero object in TerminalCategoryWithMultipleObjects( )> | ||
| B := "B" / T; | ||
| #! <A zero object in TerminalCategoryWithMultipleObjects( )> | ||
| AT := AdditiveClosure( T ); | ||
| #! AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| ABAA := [ A, B, A, A ] / AT; | ||
| #! <An object in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by 4 underlying objects> | ||
| BAB := [ B, A, B ] / AT; | ||
| #! <An object in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by 3 underlying objects> | ||
| AB := [ A, B ] / AT; | ||
| #! <An object in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by 2 underlying objects> | ||
| mor_AB := MorphismConstructor( A, "A -> B", B ); | ||
| #! <A zero, isomorphism in TerminalCategoryWithMultipleObjects( )> | ||
| mor_BA := MorphismConstructor( B, "B -> A", A ); | ||
| #! <A zero, isomorphism in TerminalCategoryWithMultipleObjects( )> | ||
| id_A := IdentityMorphism( A ); | ||
| #! <A zero, identity morphism in TerminalCategoryWithMultipleObjects( )> | ||
| id_B := IdentityMorphism( B ); | ||
| #! <A zero, identity morphism in TerminalCategoryWithMultipleObjects( )> | ||
| alpha := MorphismConstructor( ABAA, | ||
| [ [ mor_AB, id_A, mor_AB ], | ||
| [ id_B, mor_BA, id_B ], | ||
| [ mor_AB, id_A, mor_AB ], | ||
| [ mor_AB, id_A, mor_AB ] ], | ||
| BAB ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 4 x 3 matrix of underlying morphisms> | ||
| IsWellDefined( alpha ); | ||
| #! true | ||
| alpha2 := TensorProduct( alpha, alpha ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 16 x 9 matrix of underlying morphisms> | ||
| IsWellDefined( alpha2 ); | ||
| #! true | ||
| IsIsomorphism( alpha2 ); | ||
| #! true | ||
| left := LeftUnitor( ABAA ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 4 x 4 matrix of underlying morphisms> | ||
| IsWellDefined( left ); | ||
| #! true | ||
| left_inv := LeftUnitorInverse( ABAA ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 4 x 4 matrix of underlying morphisms> | ||
| IsOne( PreCompose( left, left_inv ) ); | ||
| #! true | ||
| IsOne( PreCompose( left_inv, left ) ); | ||
| #! true | ||
| right := RightUnitor( BAB ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 3 x 3 matrix of underlying morphisms> | ||
| IsWellDefined( right ); | ||
| #! true | ||
| right_inv := RightUnitorInverse( BAB ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 3 x 3 matrix of underlying morphisms> | ||
| IsOne( PreCompose( right, right_inv ) ); | ||
| #! true | ||
| IsOne( PreCompose( right_inv, right ) ); | ||
| #! true | ||
| aslr := AssociatorLeftToRight( AB, BAB, AB ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 12 x 12 matrix of underlying morphisms> | ||
| IsWellDefined( aslr ); | ||
| #! true | ||
| asrl := AssociatorRightToLeft( AB, BAB, AB ); | ||
| #! <A morphism in AdditiveClosure( TerminalCategoryWithMultipleObjects( ) ) | ||
| #! defined by a 12 x 12 matrix of underlying morphisms> | ||
| IsOne( PreCompose( aslr, asrl ) ); | ||
| #! true | ||
| IsOne( PreCompose( asrl, aslr ) ); | ||
| #! true | ||
| #! @EndExample |
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