nLab 2-category theory - contents

2-category theory

Definitions

• 2-category

• strict 2-category

• bicategory

• enriched bicategory

Transfors between 2-categories

• 2-functor

  • pseudofunctor

  • lax functor

  • equivalence of 2-categories

• 2-natural transformation

  • lax natural transformation

  • icon

• modification

• Yoneda lemma for bicategories

Morphisms in 2-categories

• fully faithful morphism

• faithful morphism

• conservative morphism

• pseudomonic morphism

• discrete morphism

• eso morphism

Structures in 2-categories

• adjunction

• mate

• monad

• cartesian object

• fibration in a 2-category

• codiscrete cofibration

Limits in 2-categories

• 2-limit

• 2-pullback

• comma object

• inserter

• inverter

• equifier

Structures on 2-categories

• 2-monad

  • lax-idempotent 2-monad

  • pseudomonad

  • pseudoalgebra for a 2-monad

• monoidal 2-category

  • cartesian bicategory

• Gray tensor product

• proarrow equipment