Category Theory :: Terms

• CT pre-reqs

  • axioms

    • identity

    • closure

    • associativity

    • commutativity

    • distributivity

    • invertability

    • idempotence

  • sets

    • cardinality

    • powerset

    • subset

    • Cartesian product

    • ordered pair

    • types of sets

      • the empty set

      • singleton set

      • unordered pair

      • 𝔹, ℕ, ℤ, ℚ, ℝ

  • relations

    • types of relations

      • empty relation

      • total relation

      • functional

      • serial

      • euclidean

    • relational axioms

      • reflexivity

      • symmetry

      • transitivity

      • trichotomy

      • (right-)unique

      • (left-)serial

    • relational closures

      • reflexive closure

      • symmetric closure

      • transitive closure

  • functions

    • sets wrt functions

      • domain

      • codomain

      • range

      • image

      • pre-image

    • properties of functions

      • injectivity

      • surjectivity

      • bijectivity

    • types

      • total

      • partial

  • abstract algebra

    • algebraic structure, algebra

      • carrier set

      • operation over the set

      • algebra axioms

    • algebraic structures

      • magma

      • semigroup

      • monoid

      • group

      • abelian group

      • ring

      • field

• CT elementary

  • category theory

  • category

  • object

  • morphism, arrow

    • identity arrow

    • composition of arrows

    • associativity of composition

  • commutative diagram

  • functor

  • types of objects

    • initial object

    • terminal object

  • types of morphism

    • isomorphism

    • homomorphism

    • epimorphism

    • monomorphism

  • types of categories

    • empty category

    • monoid

    • discrete category

    • Named categories

      • 𝗦𝗲𝘁

      • 𝗥𝗲𝗹

      • 𝗚𝗿

      • 𝗚𝗿𝗽

      • 𝗩𝗲𝗰𝘁

      • 𝗖𝗮𝘁

      • 𝗛𝗮𝘀𝗸

  • types of functors

    • endofunctor

    • identity functor

• categorical constructions

  • product

  • coproduct

• natural transformation

  • naturality

  • naturality square

• monad

  • Kleisli triple

• algebra

  • initial algebra

  • f-algebra