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.
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