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