Outline of category theory

Category theory

• Concepts

  • category

  • functor

  • natural transformation

  • Cat

• Universal constructions

  • universal construction

  • representable functor

  • adjoint functor

  • limit

  • colimit

  • weighted limit

  • end

  • coend

  • Kan extension

• Theorems

  • Yoneda lemma

  • Isbell duality

  • Grothendieck construction

  • adjoint functor theorem

  • monadicity theorem

  • adjoint lifting theorem

  • Tannaka duality

  • Gabriel-Ulmer duality

  • small object argument

  • Freyd-Mitchell embedding theorem

  • relation between type theory and category theory

• Extensions

  • sheaf and topos theory

  • enriched category theory

  • higher category theory

• Applications

  • applications of (higher) category theory