Graded Hopf algebras with basis¶
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class
sage.categories.graded_hopf_algebras_with_basis.
GradedHopfAlgebrasWithBasis
(base_category)¶ Bases:
sage.categories.graded_modules.GradedModulesCategory
The category of graded Hopf algebras with a distinguished basis.
EXAMPLES:
sage: C = GradedHopfAlgebrasWithBasis(ZZ); C Category of graded hopf algebras with basis over Integer Ring sage: C.super_categories() [Category of hopf algebras with basis over Integer Ring, Category of graded algebras with basis over Integer Ring] sage: C is HopfAlgebras(ZZ).WithBasis().Graded() True sage: C is HopfAlgebras(ZZ).Graded().WithBasis() False
TESTS:
sage: TestSuite(C).run()
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class
ElementMethods
¶
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class
GradedHopfAlgebrasWithBasis.
ParentMethods
¶
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class
GradedHopfAlgebrasWithBasis.
WithRealizations
(category, *args)¶ Bases:
sage.categories.with_realizations.WithRealizationsCategory
TESTS:
sage: from sage.categories.covariant_functorial_construction import CovariantConstructionCategory sage: class FooBars(CovariantConstructionCategory): ....: _functor_category = "FooBars" ....: _base_category_class = (Category,) sage: Category.FooBars = lambda self: FooBars.category_of(self) sage: C = FooBars(ModulesWithBasis(ZZ)) sage: C Category of foo bars of modules with basis over Integer Ring sage: C.base_category() Category of modules with basis over Integer Ring sage: latex(C) \mathbf{FooBars}(\mathbf{ModulesWithBasis}_{\Bold{Z}}) sage: import __main__; __main__.FooBars = FooBars # Fake FooBars being defined in a python module sage: TestSuite(C).run()
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super_categories
()¶ EXAMPLES:
sage: GradedHopfAlgebrasWithBasis(QQ).WithRealizations().super_categories() [Join of Category of hopf algebras over Rational Field and Category of graded algebras over Rational Field]
TESTS:
sage: TestSuite(GradedHopfAlgebrasWithBasis(QQ).WithRealizations()).run()
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class