A Syntactical Approach to Weak omega-Groupoids

Authors Thorsten Altenkirch, Ondrej Rypacek

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Thorsten Altenkirch
Ondrej Rypacek

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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)


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.
  • Type Theory
  • Category Theory
  • Higher dimensional structures


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