Graded coalgebras with basis¶

class sage.categories.graded_coalgebras_with_basis.GradedCoalgebrasWithBasis(base_category)[source]¶

Bases: GradedModulesCategory

The category of graded coalgebras with a distinguished basis.

EXAMPLES:

Sage

sage: C = GradedCoalgebrasWithBasis(QQ); C
Category of graded coalgebras with basis over Rational Field
sage: C is Coalgebras(QQ).WithBasis().Graded()
True

Python

>>> from sage.all import *
>>> C = GradedCoalgebrasWithBasis(QQ); C
Category of graded coalgebras with basis over Rational Field
>>> C is Coalgebras(QQ).WithBasis().Graded()
True

class SignedTensorProducts(category, *args)[source]¶

Bases: SignedTensorProductsCategory

The category of coalgebras with basis constructed by signed tensor product of coalgebras with basis.

extra_super_categories()[source]¶

EXAMPLES:

Sage

sage: Cat = CoalgebrasWithBasis(QQ).Graded()
sage: Cat.SignedTensorProducts().extra_super_categories()
[Category of graded coalgebras with basis over Rational Field]
sage: Cat.SignedTensorProducts().super_categories()
[Category of graded coalgebras with basis over Rational Field,
 Category of signed tensor products of graded coalgebras over Rational Field]

Python

>>> from sage.all import *
>>> Cat = CoalgebrasWithBasis(QQ).Graded()
>>> Cat.SignedTensorProducts().extra_super_categories()
[Category of graded coalgebras with basis over Rational Field]
>>> Cat.SignedTensorProducts().super_categories()
[Category of graded coalgebras with basis over Rational Field,
 Category of signed tensor products of graded coalgebras over Rational Field]