文章基本信息

标题：Category Theory in Coq 8.5
本地全文：下载
作者：Amin Timany ; Bart Jacobs
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：52
页码：30:1-30:18
DOI：10.4230/LIPIcs.FSCD.2016.30
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We report on our experience implementing category theory in Coq 8.5. Our work formalizes most of basic category theory, including concepts not covered by existing formalizations, in a library that is fit to be used as a general-purpose category-theoretical foundation. Our development particularly takes advantage of two features new to Coq 8.5: primitive projections for records and universe polymorphism. Primitive projections allow for well-behaved dualities while universe polymorphism provides a relative notion of largeness and smallness. The latter is one of the main contributions of this paper. It pushes the limits of the new universe polymorphism and constraint inference algorithm of Coq 8.5. In this paper we present in detail smallness and largeness in categories and the foundation they are built on top of. We furthermore explain how we have used the universe polymorphism of Coq 8.5 to represent smallness and largeness arguments by simply ignoring them and entrusting them to the universe inference algorithm of Coq 8.5. We also briefly discuss our experience throughout this implementation, discuss concepts formalized in this development and give a comparison with a few other developments of similar extent.
关键词：Category Theory; Coq 8.5; Universe Polymorphism; Homotopy Type Theory