Category Framework ================== The Sage Category Framework --------------------------- .. toctree:: :maxdepth: 2 sage/categories/primer sage/categories/category sage/categories/category_with_axiom sage/categories/functor sage/categories/tutorial Maps and Morphisms ------------------ .. toctree:: :maxdepth: 2 sage/categories/map sage/categories/homset sage/categories/morphism sage/categories/pushout Individual Categories --------------------- .. toctree:: :maxdepth: 2 sage/categories/action sage/categories/additive_groups sage/categories/additive_magmas sage/categories/additive_monoids sage/categories/additive_semigroups sage/categories/affine_weyl_groups sage/categories/algebra_ideals sage/categories/algebra_modules sage/categories/algebras sage/categories/algebras_with_basis sage/categories/aperiodic_semigroups sage/categories/associative_algebras sage/categories/bialgebras sage/categories/bialgebras_with_basis sage/categories/bimodules sage/categories/classical_crystals sage/categories/coalgebras sage/categories/coalgebras_with_basis sage/categories/commutative_additive_groups sage/categories/commutative_additive_monoids sage/categories/commutative_additive_semigroups sage/categories/commutative_algebra_ideals sage/categories/commutative_algebras sage/categories/commutative_ring_ideals sage/categories/commutative_rings sage/categories/complete_discrete_valuation sage/categories/complex_reflection_groups sage/categories/complex_reflection_or_generalized_coxeter_groups sage/categories/coxeter_group_algebras sage/categories/coxeter_groups sage/categories/crystals sage/categories/cw_complexes sage/categories/discrete_valuation sage/categories/distributive_magmas_and_additive_magmas sage/categories/division_rings sage/categories/domains sage/categories/enumerated_sets sage/categories/euclidean_domains sage/categories/fields sage/categories/filtered_algebras sage/categories/filtered_algebras_with_basis sage/categories/filtered_modules sage/categories/filtered_modules_with_basis sage/categories/finite_complex_reflection_groups sage/categories/finite_coxeter_groups sage/categories/finite_crystals sage/categories/finite_dimensional_algebras_with_basis sage/categories/finite_dimensional_bialgebras_with_basis sage/categories/finite_dimensional_coalgebras_with_basis sage/categories/finite_dimensional_graded_lie_algebras_with_basis sage/categories/finite_dimensional_hopf_algebras_with_basis sage/categories/finite_dimensional_lie_algebras_with_basis sage/categories/finite_dimensional_modules_with_basis sage/categories/finite_dimensional_nilpotent_lie_algebras_with_basis sage/categories/finite_dimensional_semisimple_algebras_with_basis sage/categories/finite_enumerated_sets sage/categories/finite_fields sage/categories/finite_groups sage/categories/finite_lattice_posets sage/categories/finite_monoids sage/categories/finite_permutation_groups sage/categories/finite_posets sage/categories/finite_semigroups sage/categories/finite_sets sage/categories/finite_weyl_groups sage/categories/finitely_generated_magmas sage/categories/finitely_generated_semigroups sage/categories/function_fields sage/categories/g_sets sage/categories/gcd_domains sage/categories/generalized_coxeter_groups sage/categories/graded_algebras sage/categories/graded_algebras_with_basis sage/categories/graded_bialgebras sage/categories/graded_bialgebras_with_basis sage/categories/graded_coalgebras sage/categories/graded_coalgebras_with_basis sage/categories/graded_hopf_algebras sage/categories/graded_hopf_algebras_with_basis sage/categories/graded_lie_algebras sage/categories/graded_lie_algebras_with_basis sage/categories/graded_modules sage/categories/graded_modules_with_basis sage/categories/graphs sage/categories/group_algebras sage/categories/groupoid sage/categories/groups sage/categories/hecke_modules sage/categories/highest_weight_crystals sage/categories/hopf_algebras sage/categories/hopf_algebras_with_basis sage/categories/h_trivial_semigroups sage/categories/infinite_enumerated_sets sage/categories/integral_domains sage/categories/j_trivial_semigroups sage/categories/kac_moody_algebras sage/categories/lattice_posets sage/categories/left_modules sage/categories/lie_algebras sage/categories/lie_algebras_with_basis sage/categories/lie_groups sage/categories/loop_crystals sage/categories/l_trivial_semigroups sage/categories/magmas sage/categories/magmas_and_additive_magmas sage/categories/magmatic_algebras sage/categories/manifolds sage/categories/matrix_algebras sage/categories/metric_spaces sage/categories/modular_abelian_varieties sage/categories/modules sage/categories/modules_with_basis sage/categories/monoid_algebras sage/categories/monoids sage/categories/number_fields sage/categories/objects sage/categories/partially_ordered_monoids sage/categories/permutation_groups sage/categories/pointed_sets sage/categories/polyhedra sage/categories/posets sage/categories/principal_ideal_domains sage/categories/quotient_fields sage/categories/quantum_group_representations sage/categories/regular_crystals sage/categories/regular_supercrystals sage/categories/right_modules sage/categories/ring_ideals sage/categories/rings sage/categories/rngs sage/categories/r_trivial_semigroups sage/categories/schemes sage/categories/semigroups sage/categories/semirings sage/categories/semisimple_algebras sage/categories/sets_cat sage/categories/sets_with_grading sage/categories/sets_with_partial_maps sage/categories/shephard_groups sage/categories/simplicial_complexes sage/categories/simplicial_sets sage/categories/super_algebras sage/categories/super_algebras_with_basis sage/categories/super_hopf_algebras_with_basis sage/categories/super_modules sage/categories/super_modules_with_basis sage/categories/supercommutative_algebras sage/categories/topological_spaces sage/categories/triangular_kac_moody_algebras sage/categories/unique_factorization_domains sage/categories/unital_algebras sage/categories/vector_spaces sage/categories/weyl_groups Technical Categories ~~~~~~~~~~~~~~~~~~~~ .. toctree:: :maxdepth: 2 sage/categories/facade_sets Functorial constructions ------------------------ .. toctree:: :maxdepth: 2 sage/categories/covariant_functorial_construction sage/categories/cartesian_product sage/categories/tensor sage/categories/signed_tensor sage/categories/dual sage/categories/algebra_functor sage/categories/subquotients sage/categories/quotients sage/categories/subobjects sage/categories/isomorphic_objects sage/categories/homsets sage/categories/realizations sage/categories/with_realizations Examples of parents using categories ------------------------------------- .. toctree:: :maxdepth: 2 sage/categories/examples/algebras_with_basis sage/categories/examples/commutative_additive_monoids sage/categories/examples/commutative_additive_semigroups sage/categories/examples/coxeter_groups sage/categories/examples/crystals sage/categories/examples/cw_complexes sage/categories/examples/facade_sets sage/categories/examples/finite_coxeter_groups sage/categories/examples/finite_dimensional_algebras_with_basis sage/categories/examples/finite_enumerated_sets sage/categories/examples/finite_dimensional_lie_algebras_with_basis sage/categories/examples/finite_monoids sage/categories/examples/finite_semigroups sage/categories/examples/finite_weyl_groups sage/categories/examples/graded_connected_hopf_algebras_with_basis sage/categories/examples/graded_modules_with_basis sage/categories/examples/graphs sage/categories/examples/hopf_algebras_with_basis sage/categories/examples/infinite_enumerated_sets sage/categories/examples/manifolds sage/categories/examples/lie_algebras sage/categories/examples/lie_algebras_with_basis sage/categories/examples/monoids sage/categories/examples/posets sage/categories/examples/semigroups_cython sage/categories/examples/semigroups sage/categories/examples/sets_cat sage/categories/examples/sets_with_grading sage/categories/examples/with_realizations Internals --------- .. toctree:: :maxdepth: 2 sage/categories/category_types sage/categories/category_singleton sage/categories/category_cy_helper sage/categories/coercion_methods sage/categories/poor_man_map .. include:: ../footer.txt