# 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
