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2-category theory

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Context

2-Category theory

2-category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

2-category theory is the study of 2-categories. It is the “first new level” in higher category theory.

higher category theory

Revised on March 15, 2012 15:15:24 by Urs Schreiber (82.172.178.200)
Edit | Back in time (2 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: category theory, higher category theory, axiom of choice, adjunction, 2-morphism, double category, bicategory, monad, Kan extension, representable functor, limit, span, strict 2-category, virtual double category, Gray tensor product, 2-category, two-variable adjunction, adjunct, pseudofunctor, eso morphism, fully faithful morphism, 2-limit, strict 2-limit, comma object, distributive law, idempotent monad, higher category theory and physics, (2,1)-category, hom-category, discrete object, Kan lift, lax natural transformation, modification, triangle identities, fibration in a 2-category, adjoint equivalence, lax functor, strong monad, Eilenberg-Moore category, Kleisli category, 2-category equipped with proarrows, icon, 2-functor, cartesian bicategory, 2-pullback, Yoneda lemma for bicategories, braided monoidal 2-category, Prof, cartesian object, bicategory of relations, framed bicategory, codomain fibration, canonical model structure on Cat, companion pair, whiskering, virtual equipment, 2-topos, 2Cat, monoidal bicategory, module over a monad, (infinity,1)-category theory, pseudoalgebra for a 2-monad, lax-idempotent 2-monad, vertical composition, associator, unitor, codiscrete cofibration, mate, factorization system in a 2-category, discrete morphism, faithful morphism, conservative morphism, pseudomonic morphism, 2-category theory - contents, 2-category theory, doctrinal adjunction, pseudonatural transformation, 2-site, 2-sheaf, adjoint monad, horizontal composition, unit of an adjunction, (2,1)-presheaf, strict 2-equivalence of 2-categories, biadjunction, inverter, Kleisli object, equivalence of 2-categories, Hopf adjunction, slice 2-category, 2-topos theory, vDbl, equifier, inserter, PIE-limit, two-sided fibration, isoinserter, (2,1)-sheaf, 2-adjunction, enriched bicategory, natural equivalence, full sub-2-category, locally full sub-2-category, F-category, locally fully faithful 2-functor, (infinity,2)-site, contents of contents, bicategorical trace, lax morphism, flexible limit, rigged limit, (0,1)-category theory, 2-presheaf, monad with arities, 2-trivial model structure, reflective sub-2-category, StreetCBS, 2-Giraud theorem, exact 2-category, regular 2-category, coherent 2-category, 2-pretopos, extensive 2-category, 2-congruence, table of category theories, coherence theorem for bicategories with finite limits, sylleptic monoidal 2-category, core in a 2-category, n-congruence, n-localic 2-topos, monoidal (2,1)-category, Drinfeld center