Graded Coalgebras - Category Framework

Skip to content
Back to top
View this page
Edit this page

# Graded Coalgebras

class sage.categories.graded_coalgebras.GradedCoalgebras(base_category)

  Bases: `GradedModulesCategory`

  The category of graded coalgebras.

  EXAMPLES:

  Sage

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

  Python

      >>> 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)

    Bases: `SignedTensorProductsCategory`

    extra_super_categories()

      EXAMPLES:

      Sage

          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]

      Python

          >>> 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

    Bases: `object`

    SignedTensorProducts()

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

      See also

      - `SignedTensorProductsCategory`

      - `CovariantFunctorialConstruction`

      EXAMPLES:

      Sage

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

      Python

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