
Bicategories
Title: 
Bicategories 
Author:

Eugene W. Stark (stark /at/ cs /dot/ stonybrook /dot/ edu)

Submission date: 
20200106 
Abstract: 
Taking as a starting point the author's previous work on
developing aspects of category theory in Isabelle/HOL, this article
gives a compatible formalization of the notion of
"bicategory" and develops a framework within which formal
proofs of facts about bicategories can be given. The framework
includes a number of basic results, including the Coherence Theorem,
the Strictness Theorem, pseudofunctors and biequivalence, and facts
about internal equivalences and adjunctions in a bicategory. As a
driving application and demonstration of the utility of the framework,
it is used to give a formal proof of a theorem, due to Carboni,
Kasangian, and Street, that characterizes up to biequivalence the
bicategories of spans in a category with pullbacks. The formalization
effort necessitated the fillingin of many details that were not
evident from the brief presentation in the original paper, as well as
identifying a few minor corrections along the way. 
BibTeX: 
@article{BicategoryAFP,
author = {Eugene W. Stark},
title = {Bicategories},
journal = {Archive of Formal Proofs},
month = jan,
year = 2020,
note = {\url{http://isaafp.org/entries/Bicategory.html},
Formal proof development},
ISSN = {2150914x},
}

License: 
BSD License 
Depends on: 
MonoidalCategory 
