One form of the coherence theorem for bicategories states that every bicategory is equivalent to a strict 2-category. Lack’s coherence theorem (named for Steve Lack) states that every naturally-occurring bicategory is equivalent to a naturally occurring strict 2-category. Obviously this is not a theorem in the usual sense, but rather an observation about a number of similar examples.
Instances of Lack’s coherence theorem include:
The bicategory Prof of small categories and profunctors is equivalent to the strict 2-category of presheaf categories and cocontinuous functors.
The bicategory Span(C) of spans in a category $C$ with pullbacks is equivalent to the strict 2-category of slice categories of $C$ and linear polynomial functors.
More generally, the bicategory of “polynomial data” in a locally cartesian closed category is equivalent to the strict 2-category of slices and polynomial functors.
Created on November 15, 2010 at 03:57:42. See the history of this page for a list of all contributions to it.