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A Syntactical Approach to Weak omega-Groupoids

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Abstract

When moving to a Type Theory without proof-irrelevance the notion of a setoid has to be generalized to the notion of a weak omega-groupoid. As a first step in this direction we study the formalisation of weak omega-groupoids in Type Theory. This is motivated by Voevodsky's proposal of univalent type theory which is incompatible with proof-irrelevance and the results by Lumsdaine and Garner/van de Berg showing that the standard eliminator for equality gives rise to a weak omega-groupoid.

BibTeX - Entry

@InProceedings{altenkirch_et_al:LIPIcs:2012:3656,
  author =	{Thorsten Altenkirch and Ondrej Rypacek},
  title =	{{A Syntactical Approach to Weak omega-Groupoids}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{16--30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3656},
  URN =		{urn:nbn:de:0030-drops-36561},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2012.16},
  annote =	{Keywords: Type Theory, Category Theory, Higher dimensional structures}
}

Keywords: Type Theory, Category Theory, Higher dimensional structures
Seminar: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue date: 2012
Date of publication: 2012


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