nLab category theory - contents

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

Edit this sidebar