# Bicategories

 Title: Bicategories Author: Eugene W. Stark (stark /at/ cs /dot/ stonybrook /dot/ edu) Submission date: 2020-01-06 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 filling-in 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. Change history: [2020-02-15]: Move ConcreteCategory.thy from Bicategory to Category3 and use it systematically. Make other minor improvements throughout. (revision a51840d36867) BibTeX: @article{Bicategory-AFP, author = {Eugene W. Stark}, title = {Bicategories}, journal = {Archive of Formal Proofs}, month = jan, year = 2020, note = {\url{http://isa-afp.org/entries/Bicategory.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: MonoidalCategory Status: [skipped] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.