# nLab StreetCBS

### Context

#### 2-Category theory

2-category theory

## Definitions

• 2-category

• strict 2-category

• bicategory

• enriched bicategory

• ## Transfors between 2-categories

• 2-functor

• 2-natural transformation

• 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

• mate

• 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

• monoidal 2-category

• Gray tensor product

• proarrow equipment

• #### $(\infty,2)$-Topos theory

These two papers

basically supply (via observations by Mike Shulman, see StreetCBS) definitions on the $n$Lab of regular 2-category, coherent 2-category, exact 2-category, 2-pretopos, 2-site, 2-sheaf, and Grothendieck 2-topos, as well as the proof of the 2-Giraud theorem. The definitions we are interested in are the bicategorical ones, which appear in the second paper, but the only proofs are in the first paper which does a strict version for strict 2-categories. Note in particular that where he uses the prefix “bi‑” we use either “2‑” or no prefix; thus our 2-sites are what he calles bisites, etc. There are also a couple of mistakes in the definitions and proofs which we have tried to correct in the relevant $n$Lab entries.

category: reference

Last revised on May 29, 2012 at 22:04:00. See the history of this page for a list of all contributions to it.