def super_categories(self):
"""
EXAMPLES::
sage: HopfAlgebrasWithBasis(QQ).super_categories()
[Category of bialgebras with basis over Rational Field, Category of hopf algebras over Rational Field]
"""
R = self.base_ring()
return [BialgebrasWithBasis(R), HopfAlgebras(R)]
def GradedBialgebrasWithBasis(base_ring):
"""
The category of graded bialgebras with a distinguished basis
EXAMPLES::
sage: C = GradedBialgebrasWithBasis(QQ); C
Join of Category of ...
sage: sorted(C.super_categories(), key=str)
[Category of bialgebras with basis over Rational Field,
Category of graded algebras with basis over Rational Field]
TESTS::
sage: TestSuite(C).run()
"""
from sage.categories.all import BialgebrasWithBasis
return BialgebrasWithBasis(base_ring).Graded()
def FiniteDimensionalBialgebrasWithBasis(base_ring):
"""
The category of finite dimensional bialgebras with a distinguished basis
EXAMPLES::
sage: C = FiniteDimensionalBialgebrasWithBasis(QQ); C
Category of finite dimensional bialgebras with basis over Rational Field
sage: sorted(C.super_categories(), key=str)
[Category of bialgebras with basis over Rational Field,
Category of finite dimensional algebras with basis over Rational Field]
sage: C is Bialgebras(QQ).WithBasis().FiniteDimensional()
True
TESTS::
sage: TestSuite(C).run()
"""
from sage.categories.all import BialgebrasWithBasis
return BialgebrasWithBasis(base_ring).FiniteDimensional()