Category Framework¶
Introduction¶
The Sage Category Framework¶
Maps and Morphisms¶
Individual Categories¶
- 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
Technical Categories¶
Functorial constructions¶
- 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 parents using categories¶
- 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