Bialgebras¶
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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()
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class
ElementMethods
¶
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class
Bialgebras.
ParentMethods
¶
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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
Todo
This category should be a
CategoryWithAxiom
.EXAMPLES:
sage: Bialgebras(QQ).additional_structure()
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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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class