Graded coalgebras with basis - Category Framework

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# Graded coalgebras with basis

class sage.categories.graded_coalgebras_with_basis.GradedCoalgebrasWithBasis(base_category)

  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)

    Bases: `SignedTensorProductsCategory`

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

    extra_super_categories()

      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]