def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: from sage.geometry.hyperbolic_space.hyperbolic_interface import HyperbolicModels
sage: H = HyperbolicPlane()
sage: models = HyperbolicModels(H)
sage: models.super_categories()
[Category of sets, Category of realizations of Hyperbolic plane]
"""
return [Sets(), Realizations(self.base())]
def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: from sage.combinat.descent_algebra import DescentAlgebraBases
sage: DA = DescentAlgebra(QQ, 4)
sage: bases = DescentAlgebraBases(DA)
sage: bases.super_categories()
[Category of finite dimensional algebras with basis over Rational Field,
Category of realizations of Descent algebra of 4 over Rational Field]
"""
return [self.base()._category, Realizations(self.base())]
def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: from sage.algebras.lie_algebras.free_lie_algebra import FreeLieAlgebraBases
sage: L.<x, y> = LieAlgebra(QQ)
sage: bases = FreeLieAlgebraBases(L)
sage: bases.super_categories()
[Category of lie algebras with basis over Rational Field,
Category of realizations of Free Lie algebra generated by (x, y) over Rational Field]
"""
return [LieAlgebras(self.base().base_ring()).WithBasis(), Realizations(self.base())]
def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: from sage.combinat.posets.moebius_algebra import MoebiusAlgebraBases
sage: M = posets.BooleanLattice(4).moebius_algebra(QQ)
sage: bases = MoebiusAlgebraBases(M)
sage: bases.super_categories()
[Category of finite dimensional commutative algebras with basis over Rational Field,
Category of realizations of Moebius algebra of Finite lattice
containing 16 elements over Rational Field]
"""
return [self.base()._category, Realizations(self.base())]
def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: from sage.combinat.fqsym import FQSymBases
sage: FQSym = algebras.FQSym(ZZ)
sage: bases = FQSymBases(FQSym)
sage: bases.super_categories()
[Category of graded connected hopf algebras with basis over Integer Ring,
Category of realizations of Free Quasi-symmetric functions over Integer Ring]
"""
return [
self.base()._category.WithBasis().Graded(),
Realizations(self.base())
]
def super_categories(self):
r"""
The super categories of ``self``.
EXAMPLES::
sage: Sym = SymmetricFunctions(QQ['t'])
sage: from sage.combinat.sf.new_kschur import KBoundedSubspaceBases
sage: KB = Sym.kBoundedSubspace(3)
sage: KBB = KBoundedSubspaceBases(KB); KBB
Category of k bounded subspace bases of 3-bounded Symmetric Functions over Univariate Polynomial Ring in t over Rational Field
sage: KBB.super_categories()
[Category of realizations of 3-bounded Symmetric Functions over Univariate Polynomial Ring in t over Rational Field, Join of Category of graded coalgebras with basis over Univariate Polynomial Ring in t over Rational Field and Category of subobjects of sets]
"""
R = self.base().base_ring()
category = GradedHopfAlgebrasWithBasis(R) if self.t == 1 else GradedCoalgebrasWithBasis(R)
return [Realizations(self.base()), category.Subobjects()]