Graded Coalgebras#

class sage.categories.graded_coalgebras.GradedCoalgebras(base_category)[source]#

Bases: GradedModulesCategory

The category of graded coalgebras

EXAMPLES:

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

C = GradedCoalgebras(QQ); C
C is Coalgebras(QQ).Graded()
>>> from sage.all import *
>>> C = GradedCoalgebras(QQ); C
Category of graded coalgebras over Rational Field
>>> C is Coalgebras(QQ).Graded()
True
class SignedTensorProducts(category, *args)[source]#

Bases: SignedTensorProductsCategory

extra_super_categories()[source]#

EXAMPLES:

sage: Coalgebras(QQ).Graded().SignedTensorProducts().extra_super_categories()
[Category of graded coalgebras over Rational Field]
sage: Coalgebras(QQ).Graded().SignedTensorProducts().super_categories()
[Category of graded coalgebras over Rational Field]

Coalgebras(QQ).Graded().SignedTensorProducts().extra_super_categories()
Coalgebras(QQ).Graded().SignedTensorProducts().super_categories()
>>> from sage.all import *
>>> Coalgebras(QQ).Graded().SignedTensorProducts().extra_super_categories()
[Category of graded coalgebras over Rational Field]
>>> Coalgebras(QQ).Graded().SignedTensorProducts().super_categories()
[Category of graded coalgebras over Rational Field]

Meaning: a signed tensor product of coalgebras is a coalgebra

class SubcategoryMethods[source]#

Bases: object

SignedTensorProducts()[source]#

Return the full subcategory of objects of self constructed as signed tensor products.

See also

EXAMPLES:

sage: CoalgebrasWithBasis(QQ).Graded().SignedTensorProducts()
Category of signed tensor products of graded coalgebras with basis
 over Rational Field

CoalgebrasWithBasis(QQ).Graded().SignedTensorProducts()
>>> from sage.all import *
>>> CoalgebrasWithBasis(QQ).Graded().SignedTensorProducts()
Category of signed tensor products of graded coalgebras with basis
 over Rational Field