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Bicategories
Title: |
Bicategories |
Author:
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Eugene W. Stark (stark /at/ cs /dot/ stonybrook /dot/ edu)
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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)
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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},
}
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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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