Bialgebras#
- class sage.categories.bialgebras.Bialgebras(base, name=None)#
Bases:
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]
- class ElementMethods#
Bases:
object
- is_grouplike()#
Return whether
self
is a grouplike element.EXAMPLES:
sage: s = SymmetricFunctions(QQ).schur() sage: s([5]).is_grouplike() False sage: s([]).is_grouplike() True
- is_primitive()#
Return whether
self
is a primitive element.EXAMPLES:
sage: s = SymmetricFunctions(QQ).schur() sage: s([5]).is_primitive() False sage: p = SymmetricFunctions(QQ).powersum() sage: p([5]).is_primitive() True
- class Super(base_category)#
Bases:
SuperModulesCategory
- WithBasis#
alias of
BialgebrasWithBasis
- 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()
- super_categories()#
EXAMPLES:
sage: Bialgebras(QQ).super_categories() [Category of algebras over Rational Field, Category of coalgebras over Rational Field]