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# Bialgebras

class `sage.categories.bialgebras.``Bialgebras`(base, name=None)

  Bases: `sage.categories.category_types.Category_over_base_ring`

  The category of bialgebras

  EXAMPLES:

      sage: Bialgebras(ZZ)
      Category of bialgebras over Integer Ring
      sage: Bialgebras(ZZ).super_categories()
      [Category of algebras over Integer Ring, Category of coalgebras over Integer Ring]

  TESTS:

      sage: TestSuite(Bialgebras(ZZ)).run()

  class `ElementMethods`
  class `Bialgebras.``ParentMethods`
  `Bialgebras.``additional_structure`()

    Return `None`.

    Indeed, the category of bialgebras defines no additional structure: a morphism of coalgebras and of algebras between two bialgebras is a bialgebra morphism.

    See also

    `Category.additional_structure()`

    Todo

    This category should be a `CategoryWithAxiom`.

    EXAMPLES:

        sage: Bialgebras(QQ).additional_structure()

  `Bialgebras.``super_categories`()

    EXAMPLES:

        sage: Bialgebras(QQ).super_categories()
        [Category of algebras over Rational Field, Category of coalgebras over Rational Field]

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