License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TYPES.2017.7
URN: urn:nbn:de:0030-drops-100553
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/10055/
Palmgren, Erik
On Equality of Objects in Categories in Constructive Type Theory
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}
}
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Keywords: |
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type theory, formalization, category theory, setoids |
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Collection: |
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23rd International Conference on Types for Proofs and Programs (TYPES 2017) |
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Issue Date: |
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2018 |
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Date of publication: |
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08.01.2019 |
