Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Palmgren, Erik https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-100553
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On Equality of Objects in Categories in Constructive Type Theory

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Abstract

In this note we remark on the problem of equality of objects in categories formalized in Martin-Löf's constructive type theory. A standard notion of category in this system is E-category, where no such equality is specified. The main observation here is that there is no general extension of E-categories to categories with equality on objects, unless the principle Uniqueness of Identity Proofs (UIP) holds. We also introduce the notion of an H-category with equality on objects, which makes it easy to compare to the notion of univalent category proposed for Univalent Type Theory by Ahrens, Kapulkin and Shulman.

BibTeX - Entry

@InProceedings{palmgren:LIPIcs:2018:10055,
  author =	{Erik Palmgren},
  title =	{{On Equality of Objects in Categories in Constructive Type Theory}},
  booktitle =	{23rd International Conference on Types for Proofs and  Programs (TYPES 2017)},
  pages =	{7:1--7:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-071-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{104},
  editor =	{Andreas Abel and Fredrik Nordvall Forsberg and Ambrus Kaposi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10055},
  URN =		{urn:nbn:de:0030-drops-100553},
  doi =		{10.4230/LIPIcs.TYPES.2017.7},
  annote =	{Keywords: type theory, formalization, category theory, setoids}
}

Keywords: type theory, formalization, category theory, setoids
Seminar: 23rd International Conference on Types for Proofs and Programs (TYPES 2017)
Issue date: 2018
Date of publication: 08.01.2019


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