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