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A Syntactical Approach to Weak omega-Groupoids Altenkirch, Thorsten Rypacek, Ondrej Type Theory Category Theory Higher dimensional structures 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thorsten Altenkirch and Ondrej Rypacek 2012 Is Part Of LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2012.16 urn:nbn:de:0030-drops-36561 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.16 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode