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from __future__ import absolute_import 

from sage.misc.lazy_import import lazy_import 

 

from .category import Category 

 

from .category_types import( 

Elements, 

ChainComplexes, 

) 

 

from sage.categories.simplicial_complexes import SimplicialComplexes 

 

from .tensor import tensor 

from .cartesian_product import cartesian_product 

 

from .functor import (ForgetfulFunctor, 

IdentityFunctor) 

 

from .homset import (Hom, hom, 

End, end, 

Homset, HomsetWithBase) 

 

from .morphism import Morphism 

 

from .basic import * 

 

from .realizations import Realizations 

 

from .g_sets import GSets 

from .pointed_sets import PointedSets 

 

from .sets_with_partial_maps import SetsWithPartialMaps 

from .sets_with_grading import SetsWithGrading 

 

from .groupoid import Groupoid 

from .permutation_groups import PermutationGroups 

 

# enumerated sets 

from .finite_sets import FiniteSets 

from .enumerated_sets import EnumeratedSets 

from .finite_enumerated_sets import FiniteEnumeratedSets 

from .infinite_enumerated_sets import InfiniteEnumeratedSets 

 

# posets 

from .posets import Posets 

from .finite_posets import FinitePosets 

from .lattice_posets import LatticePosets 

from .finite_lattice_posets import FiniteLatticePosets 

 

# finite groups/... 

from .finite_semigroups import FiniteSemigroups 

from .finite_monoids import FiniteMonoids 

from .finite_groups import FiniteGroups 

from .finite_permutation_groups import FinitePermutationGroups 

 

# fields 

from .number_fields import NumberFields 

from .function_fields import FunctionFields 

 

# modules 

from .left_modules import LeftModules 

from .right_modules import RightModules 

from .bimodules import Bimodules 

 

from .modules import Modules 

RingModules = Modules 

from .vector_spaces import VectorSpaces 

 

# (hopf) algebra structures 

from .algebras import Algebras 

from .commutative_algebras import CommutativeAlgebras 

from .coalgebras import Coalgebras 

from .bialgebras import Bialgebras 

from .hopf_algebras import HopfAlgebras 

from .lie_algebras import LieAlgebras 

 

# specific algebras 

from .monoid_algebras import MonoidAlgebras 

from .group_algebras import GroupAlgebras 

from .matrix_algebras import MatrixAlgebras 

 

# ideals 

from .ring_ideals import RingIdeals 

Ideals = RingIdeals 

from .commutative_ring_ideals import CommutativeRingIdeals 

from .algebra_modules import AlgebraModules 

from .algebra_ideals import AlgebraIdeals 

from .commutative_algebra_ideals import CommutativeAlgebraIdeals 

 

# schemes and varieties 

from .modular_abelian_varieties import ModularAbelianVarieties 

from .schemes import Schemes 

 

# * with basis 

from .modules_with_basis import ModulesWithBasis 

FreeModules = ModulesWithBasis 

from .hecke_modules import HeckeModules 

from .algebras_with_basis import AlgebrasWithBasis 

from .coalgebras_with_basis import CoalgebrasWithBasis 

from .bialgebras_with_basis import BialgebrasWithBasis 

from .hopf_algebras_with_basis import HopfAlgebrasWithBasis 

 

# finite dimensional * with basis 

from .finite_dimensional_modules_with_basis import FiniteDimensionalModulesWithBasis 

from .finite_dimensional_algebras_with_basis import FiniteDimensionalAlgebrasWithBasis 

from .finite_dimensional_coalgebras_with_basis import FiniteDimensionalCoalgebrasWithBasis 

from .finite_dimensional_bialgebras_with_basis import FiniteDimensionalBialgebrasWithBasis 

from .finite_dimensional_hopf_algebras_with_basis import FiniteDimensionalHopfAlgebrasWithBasis 

 

# graded * 

from .graded_modules import GradedModules 

from .graded_algebras import GradedAlgebras 

from .graded_coalgebras import GradedCoalgebras 

from .graded_bialgebras import GradedBialgebras 

from .graded_hopf_algebras import GradedHopfAlgebras 

 

# graded * with basis 

from .graded_modules_with_basis import GradedModulesWithBasis 

from .graded_algebras_with_basis import GradedAlgebrasWithBasis 

from .graded_coalgebras_with_basis import GradedCoalgebrasWithBasis 

from .graded_bialgebras_with_basis import GradedBialgebrasWithBasis 

from .graded_hopf_algebras_with_basis import GradedHopfAlgebrasWithBasis 

 

# Coxeter groups 

from .coxeter_groups import CoxeterGroups 

lazy_import('sage.categories.finite_coxeter_groups', 'FiniteCoxeterGroups') 

from .weyl_groups import WeylGroups 

from .finite_weyl_groups import FiniteWeylGroups 

from .affine_weyl_groups import AffineWeylGroups 

 

# crystal bases 

from .crystals import Crystals 

from .highest_weight_crystals import HighestWeightCrystals 

from .regular_crystals import RegularCrystals 

from .finite_crystals import FiniteCrystals 

from .classical_crystals import ClassicalCrystals 

 

# polyhedra 

lazy_import('sage.categories.polyhedra', 'PolyhedralSets')