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()]