Category Theory

• Elements, parents, and categories in Sage: a (draft of) primer
  • Abstract
  • Introduction
  • Object oriented programming paradigm
  • Elements, Parents, Categories
  • Generic tests
  • Advanced algebraic structures
  • Functorial constructions
  • Dynamic hierarchies for categories and classes
  • Writing a new category
  • Caveats
• Implementing a new parent: a (draft of) tutorial
• Categories
• Specific category classes.
• Homsets
• Morphisms
• Functors

Functorial constructions

• Covariant Functorial Constructions
• Cartesian Product Functorial Construction
• Tensor Product Functorial Construction
• Dual functorial construction
• Algebra Functorial Construction
• Subquotient Functorial Construction
• Quotients Functorial Construction
• Subobjects Functorial Construction
• Isomorphic Objects Functorial Construction

Categories

• Additive Magmas
• AlgebraIdeals
• AlgebraModules
• Algebras
• Algebras With Basis
• Bialgebras
• BialgebrasWithBasis
• Bimodules
• Classical Crystals
• Coalgebras
• CoalgebrasWithBasis
• CommutativeAdditiveGroups
• CommutativeAdditiveMonoids
• CommutativeAdditiveSemigroups
• CommutativeAlgebraIdeals
• CommutativeAlgebras
• CommutativeRingIdeals
• CommutativeRings
• Coxeter Groups
• Crystals
• DivisionRings
• Domains
• Enumerated Sets
• EuclideanDomains
• Fields
• Finite Crystals
• Finite Coxeter Groups
• FiniteDimensionalAlgebrasWithBasis
• FiniteDimensionalBialgebrasWithBasis
• FiniteDimensionalCoalgebrasWithBasis
• FiniteDimensionalHopfAlgebrasWithBasis
• FiniteDimensionalModulesWithBasis
• Finite Enumerated Sets
• Finite Fields
• Finite Monoids
• Finite Permutation Groups
• FiniteSemigroups
• Finite Weyl Groups
• GcdDomains
• Graded Algebras
• GradedAlgebrasWithBasis
• GradedBialgebras
• GradedBialgebrasWithBasis
• Graded Coalgebras
• GradedCoalgebrasWithBasis
• Graded Hopf algebras
• GradedHopfAlgebrasWithBasis
• GradedModules
• GradedModulesWithBasis
• Groupoid
• Groups
• G-Sets
• Hecke modules
• Highest Weight Crystals
• HopfAlgebras
• HopfAlgebrasWithBasis
• Infinite Enumerated Sets
• IntegralDomains
• LeftModules
• Magmas
• MatrixAlgebras
• ModularAbelianVarieties
• Modules
• Modules With Basis
• MonoidAlgebras
• Monoids
• NumberFields
• Objects
• PartiallyOrderedMonoids
• PartiallyOrderedSets
• PointedSets
• PrincipalIdealDomains
• QuotientFields
• RightModules
• RingIdeals
• Rings
• Rngs
• Schemes
• Semigroups
• Semirings
• Sets
• UniqueFactorizationDomains
• Vector Spaces
• Weyl Groups

Examples of parents using categories

• Examples of algebras with basis
• Examples of commutative additive monoids
• Examples of commutative additive semigroups
• Examples of Coxeter groups
• Examples of finite Coxeter groups
• Examples of finite enumerated sets
• Examples of finite monoids
• Examples of finite semigroups
• Examples of finite Weyl groups
• Examples of algebras with basis
• Examples of infinite enumerated sets
• Examples of monoids
• Examples of semigroups
• Examples of semigroups in cython
• Examples of sets