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.

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