Sage Reference Manual

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Category Theory
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===============
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.. toctree::
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   :maxdepth: 2
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   sage/categories/primer
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   sage/categories/tutorial
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   sage/categories/category
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   sage/categories/category_types
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   sage/categories/category_singleton
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   sage/categories/category_with_axiom
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   sage/categories/map
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   sage/categories/homset
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   sage/categories/morphism
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   sage/categories/functor
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   sage/categories/pushout
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Functorial constructions
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========================
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.. toctree::
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   :maxdepth: 2
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   sage/categories/covariant_functorial_construction
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   sage/categories/cartesian_product
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   sage/categories/tensor
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   sage/categories/dual
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   sage/categories/algebra_functor
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   sage/categories/subquotients
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   sage/categories/quotients
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   sage/categories/subobjects
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   sage/categories/isomorphic_objects
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   sage/categories/homsets
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   sage/categories/realizations
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   sage/categories/with_realizations
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Categories
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==========
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.. toctree::
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   :maxdepth: 2
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   sage/categories/additive_groups
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   sage/categories/additive_magmas
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   sage/categories/additive_monoids
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   sage/categories/additive_semigroups
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   sage/categories/affine_weyl_groups
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   sage/categories/algebra_ideals
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   sage/categories/algebra_modules
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   sage/categories/algebras
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   sage/categories/algebras_with_basis
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   sage/categories/associative_algebras
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   sage/categories/bialgebras
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   sage/categories/bialgebras_with_basis
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   sage/categories/bimodules
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   sage/categories/classical_crystals
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   sage/categories/coalgebras
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   sage/categories/coalgebras_with_basis
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   sage/categories/commutative_additive_groups
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   sage/categories/commutative_additive_monoids
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   sage/categories/commutative_additive_semigroups
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   sage/categories/commutative_algebra_ideals
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   sage/categories/commutative_algebras
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   sage/categories/commutative_ring_ideals
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   sage/categories/commutative_rings
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   sage/categories/complete_discrete_valuation
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   sage/categories/coxeter_group_algebras
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   sage/categories/coxeter_groups
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   sage/categories/crystals
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   sage/categories/discrete_valuation
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   sage/categories/distributive_magmas_and_additive_magmas
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   sage/categories/division_rings
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   sage/categories/domains
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   sage/categories/enumerated_sets
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   sage/categories/euclidean_domains
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   sage/categories/fields
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   sage/categories/finite_coxeter_groups
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   sage/categories/finite_crystals
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   sage/categories/finite_dimensional_algebras_with_basis
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   sage/categories/finite_dimensional_bialgebras_with_basis
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   sage/categories/finite_dimensional_coalgebras_with_basis
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   sage/categories/finite_dimensional_hopf_algebras_with_basis
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   sage/categories/finite_dimensional_modules_with_basis
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   sage/categories/finite_dimensional_semisimple_algebras_with_basis
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   sage/categories/finite_enumerated_sets
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   sage/categories/finite_fields
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   sage/categories/finite_groups
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   sage/categories/finite_lattice_posets
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   sage/categories/finite_monoids
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   sage/categories/finite_permutation_groups
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   sage/categories/finite_posets
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   sage/categories/finite_semigroups
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   sage/categories/finite_sets
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   sage/categories/finite_weyl_groups
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   sage/categories/function_fields
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   sage/categories/g_sets
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   sage/categories/gcd_domains
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   sage/categories/graded_algebras
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   sage/categories/graded_algebras_with_basis
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   sage/categories/graded_bialgebras
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   sage/categories/graded_bialgebras_with_basis
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   sage/categories/graded_coalgebras
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   sage/categories/graded_coalgebras_with_basis
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   sage/categories/graded_hopf_algebras
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   sage/categories/graded_hopf_algebras_with_basis
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   sage/categories/graded_modules
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   sage/categories/graded_modules_with_basis
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   sage/categories/group_algebras
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   sage/categories/groupoid
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   sage/categories/groups
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   sage/categories/hecke_modules
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   sage/categories/highest_weight_crystals
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   sage/categories/hopf_algebras
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   sage/categories/hopf_algebras_with_basis
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   sage/categories/infinite_enumerated_sets
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   sage/categories/integral_domains
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   sage/categories/lattice_posets
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   sage/categories/left_modules
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   sage/categories/magmas
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   sage/categories/magmas_and_additive_magmas
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   sage/categories/magmatic_algebras
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   sage/categories/matrix_algebras
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   sage/categories/modular_abelian_varieties
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   sage/categories/modules
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   sage/categories/modules_with_basis
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   sage/categories/monoid_algebras
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   sage/categories/monoids
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   sage/categories/number_fields
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   sage/categories/objects
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   sage/categories/partially_ordered_monoids
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   sage/categories/permutation_groups
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   sage/categories/pointed_sets
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   sage/categories/polyhedra
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   sage/categories/posets
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   sage/categories/principal_ideal_domains
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   sage/categories/quotient_fields
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   sage/categories/regular_crystals
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   sage/categories/right_modules
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   sage/categories/ring_ideals
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   sage/categories/rings
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   sage/categories/rngs
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   sage/categories/schemes
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   sage/categories/semigroups
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   sage/categories/semirings
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   sage/categories/semisimple_algebras
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   sage/categories/sets_cat
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   sage/categories/sets_with_grading
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   sage/categories/sets_with_partial_maps
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   sage/categories/unique_factorization_domains
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   sage/categories/unital_algebras
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   sage/categories/vector_spaces
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   sage/categories/weyl_groups
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Technical Categories
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====================
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.. toctree::
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   :maxdepth: 2
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   sage/categories/facade_sets
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Examples of parents using categories
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=====================================
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.. toctree::
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   :maxdepth: 2
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   sage/categories/examples/algebras_with_basis
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   sage/categories/examples/commutative_additive_monoids
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   sage/categories/examples/commutative_additive_semigroups
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   sage/categories/examples/coxeter_groups
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   sage/categories/examples/crystals
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   sage/categories/examples/facade_sets
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   sage/categories/examples/finite_coxeter_groups
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   sage/categories/examples/finite_enumerated_sets
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   sage/categories/examples/finite_monoids
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   sage/categories/examples/finite_semigroups
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   sage/categories/examples/finite_weyl_groups
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   sage/categories/examples/graded_modules_with_basis
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   sage/categories/examples/hopf_algebras_with_basis
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   sage/categories/examples/infinite_enumerated_sets
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   sage/categories/examples/monoids
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   sage/categories/examples/posets
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   sage/categories/examples/semigroups_cython
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   sage/categories/examples/semigroups
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   sage/categories/examples/sets_cat
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   sage/categories/examples/sets_with_grading
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   sage/categories/examples/with_realizations
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Miscellaneous
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=============
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.. toctree::
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   :maxdepth: 2
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   sage/categories/action
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   sage/categories/category_cy_helper
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   sage/categories/poor_man_map
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.. include:: ../footer.txt
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