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A Syntactical Approach to Weak omega-Groupoids

Authors: Thorsten Altenkirch and Ondrej Rypacek

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)


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.

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Thorsten Altenkirch and Ondrej Rypacek. A Syntactical Approach to Weak omega-Groupoids. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 16-30, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)


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@InProceedings{altenkirch_et_al:LIPIcs.CSL.2012.16,
  author =	{Altenkirch, Thorsten and Rypacek, Ondrej},
  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 =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.16},
  URN =		{urn:nbn:de:0030-drops-36561},
  doi =		{10.4230/LIPIcs.CSL.2012.16},
  annote =	{Keywords: Type Theory, Category Theory, Higher dimensional structures}
}
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