.. _ch:categories: Category Theory =============== .. toctree:: :maxdepth: 2 sage/categories/primer sage/categories/tutorial sage/categories/category sage/categories/category_types sage/categories/map sage/categories/homset sage/categories/morphism sage/categories/functor sage/categories/pushout Functorial constructions ======================== .. toctree:: :maxdepth: 2 sage/categories/covariant_functorial_construction sage/categories/cartesian_product sage/categories/tensor sage/categories/dual sage/categories/algebra_functor sage/categories/subquotients sage/categories/quotients sage/categories/subobjects sage/categories/isomorphic_objects sage/categories/realizations sage/categories/with_realizations Categories ========== .. toctree:: :maxdepth: 2 sage/categories/additive_magmas sage/categories/algebra_ideals sage/categories/algebra_modules sage/categories/algebras sage/categories/algebras_with_basis 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/coxeter_groups sage/categories/crystals sage/categories/division_rings sage/categories/domains sage/categories/enumerated_sets sage/categories/euclidean_domains sage/categories/fields sage/categories/finite_crystals sage/categories/finite_coxeter_groups 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_hopf_algebras_with_basis sage/categories/finite_dimensional_modules_with_basis sage/categories/finite_enumerated_sets sage/categories/finite_fields sage/categories/finite_posets sage/categories/finite_lattice_posets sage/categories/finite_monoids sage/categories/finite_permutation_groups sage/categories/finite_semigroups sage/categories/finite_weyl_groups sage/categories/gcd_domains 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_modules sage/categories/graded_modules_with_basis sage/categories/groupoid sage/categories/groups sage/categories/g_sets sage/categories/hecke_modules sage/categories/highest_weight_crystals sage/categories/hopf_algebras sage/categories/hopf_algebras_with_basis sage/categories/infinite_enumerated_sets sage/categories/integral_domains sage/categories/lattice_posets sage/categories/left_modules sage/categories/magmas sage/categories/matrix_algebras 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/posets sage/categories/pointed_sets sage/categories/principal_ideal_domains sage/categories/quotient_fields sage/categories/right_modules sage/categories/ring_ideals sage/categories/rings sage/categories/rngs sage/categories/schemes sage/categories/semigroups sage/categories/semirings sage/categories/sets_cat sage/categories/unique_factorization_domains sage/categories/vector_spaces sage/categories/weyl_groups Technical Categories ==================== .. toctree:: :maxdepth: 2 sage/categories/facade_sets 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/finite_coxeter_groups sage/categories/examples/finite_enumerated_sets sage/categories/examples/finite_monoids sage/categories/examples/finite_semigroups sage/categories/examples/finite_weyl_groups sage/categories/examples/hopf_algebras_with_basis sage/categories/examples/infinite_enumerated_sets sage/categories/examples/monoids sage/categories/examples/semigroups sage/categories/examples/semigroups_cython sage/categories/examples/sets_cat sage/categories/examples/with_realizations Miscellaneous ============= .. toctree:: :maxdepth: 2 sage/categories/action
