nLab coherence theorem for bicategories with finite limits


2-Category theory

Limits and colimits



(Power) Any bicategory with finite bilimits is equivalent to a strict 2-category with finite flexible limits.


Let KK be a bicategory with finite bilimits, let K[K op,Cat]K \hookrightarrow [K^{op},Cat] be its Yoneda embedding, and let KK' be the closure of KK in [K op,Cat][K^{op},Cat] under finite flexible limits. Since CatCat is a strict 2-category with finite flexible limits, so is [K op,Cat][K^{op},Cat]. And since KK has finite bilimits, and these are preserved by its Yoneda embedding, while flexible limits are in particular bilimits, every object of KK' is equivalent to an object of KK. Thus, KKK\simeq K'.


Last revised on August 14, 2017 at 04:41:31. See the history of this page for a list of all contributions to it.