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Category Framework

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Version 10.5 Reference Manual

Home - Category Framework

Sage categories quickref

Elements, parents, and categories in Sage: a primer
Categories
Axioms
Functors
Implementing a new parent: a tutorial

Base class for maps
Homsets
Morphisms
Coercion via construction functors

Group, ring, etc. actions on objects
Additive groups
Additive magmas
Additive monoids
Additive semigroups
Affine Weyl groups
Algebra ideals
Algebra modules
Algebras
Algebras With Basis
Aperiodic semigroups
Associative algebras
Bialgebras
Bialgebras with basis
Bimodules
Classical Crystals
Coalgebras
Coalgebras with basis
Commutative additive groups
Commutative additive monoids
Commutative additive semigroups
Commutative algebra ideals
Commutative algebras
Commutative ring ideals
Commutative rings
Complete Discrete Valuation Rings (CDVR) and Fields (CDVF)
Complex reflection groups
Common category for Generalized Coxeter Groups or Complex Reflection Groups
Coxeter Group Algebras
Coxeter Groups
Crystals
CW Complexes
Discrete Valuation Rings (DVR) and Fields (DVF)
Distributive Magmas and Additive Magmas
Division rings
Domains
Enumerated sets
Euclidean domains
Fields
Filtered Algebras
Filtered Algebras With Basis
Filtered Modules
Filtered Modules With Basis
Finite Complex Reflection Groups
Finite Coxeter Groups
Finite Crystals
Finite dimensional algebras with basis
Finite dimensional bialgebras with basis
Finite dimensional coalgebras with basis
Finite Dimensional Graded Lie Algebras With Basis
Finite dimensional Hopf algebras with basis
Finite Dimensional Lie Algebras With Basis
Finite dimensional modules with basis
Finite Dimensional Nilpotent Lie Algebras With Basis
Finite dimensional semisimple algebras with basis
Finite Enumerated Sets
Finite fields
Finite groups
Finite lattice posets
Finite monoids
Finite Permutation Groups
Finite posets
Finite semigroups
Finite sets
Finite Weyl Groups
Finitely Generated Lambda bracket Algebras
Finitely Generated Lie Conformal Algebras
Finitely generated magmas
Finitely generated semigroups
Function fields
G-Sets
Gcd domains
Generalized Coxeter Groups
Graded Algebras
Graded algebras with basis
Graded bialgebras
Graded bialgebras with basis
Graded Coalgebras
Graded coalgebras with basis
Graded Hopf algebras
Graded Hopf algebras with basis
Graded Lie Algebras
Graded Lie Algebras With Basis
Graded Lie Conformal Algebras
Graded modules
Graded modules with basis
Graphs
Group Algebras
Groupoid
Groups
Hecke modules
Highest Weight Crystals
Hopf algebras
Hopf algebras with basis
H-trivial semigroups
Infinite Enumerated Sets
Integral domains
J-trivial semigroups
Kac-Moody Algebras
Lambda Bracket Algebras
Lambda Bracket Algebras With Basis
Lattice posets
Left modules
Lie Algebras
Lie Algebras With Basis
Lie Conformal Algebras
Lie Conformal Algebras With Basis
Lie Groups
Loop Crystals
L-trivial semigroups
Magmas
Magmas and Additive Magmas
Non-unital non-associative algebras
Manifolds
Matrix algebras
Metric Spaces
Modular abelian varieties
Modules
Modules With Basis
Monoid algebras
Monoids
Number fields
Objects
Partially ordered monoids
Permutation groups
Pointed sets
Polyhedral subsets of free ZZ, QQ or RR-modules.
Posets
Principal ideal domains
Quotient fields
Quantum Group Representations
Regular Crystals
Regular Supercrystals
Right modules
Ring ideals
Rings
Rngs
R-trivial semigroups
Schemes
Semigroups
Semirngs
Semisimple Algebras
Sets
Sets With a Grading
SetsWithPartialMaps
Shephard Groups
Simplicial Complexes
Simplicial Sets
Super Algebras
Super algebras with basis
Super Hopf algebras with basis
Super Lie Conformal Algebras
Super modules
Super modules with basis
Supercommutative Algebras
Supercrystals
Topological Spaces
Kac-Moody Algebras With Triangular Decomposition Basis
Unique factorization domains
Unital algebras
Vector Bundles
Vector Spaces
Weyl Groups

Facade Sets

Covariant Functorial Constructions
Cartesian Product Functorial Construction
Tensor Product Functorial Construction
Signed Tensor Product Functorial Construction
Dual functorial construction
Group algebras and beyond: the Algebra functorial construction
Subquotient Functorial Construction
Quotients Functorial Construction
Subobjects Functorial Construction
Isomorphic Objects Functorial Construction
Homset categories
Realizations Covariant Functorial Construction
With Realizations Covariant Functorial Construction

Examples of algebras with basis
Examples of commutative additive monoids
Examples of commutative additive semigroups
Examples of Coxeter groups
Example of a crystal
Examples of CW complexes
Example of facade set
Examples of finite Coxeter groups
Example of a finite dimensional algebra with basis
Examples of a finite dimensional Lie algebra with basis
Examples of finite enumerated sets
Examples of finite monoids
Examples of finite semigroups
Examples of finite Weyl groups
Examples of graded connected Hopf algebras with basis
Examples of graded modules with basis
Examples of graphs
Examples of Hopf algebras with basis
Examples of infinite enumerated sets
Examples of a Lie algebra
Examples of a Lie algebra with basis
Examples of magmas
Examples of manifolds
Examples of monoids
Examples of posets
Examples of semigroups
Examples of semigroups in cython
Examples of sets
Example of a set with grading
Examples of parents endowed with multiple realizations

Specific category classes
Singleton categories
Fast functions for the category framework
Coercion methods for categories
Poor Man’s map

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Examples of Coxeter groups¶

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