.. _ch:categories:

Category Theory
===============

.. toctree::
   :maxdepth: 2

   sage/categories/primer
   sage/categories/tutorial
   sage/categories/category
   sage/categories/category_types
   sage/categories/homset
   sage/categories/morphism
   sage/categories/functor

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

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_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/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/partially_ordered_sets
   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

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/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