Some constructions on ω-groupoids
Altenkirch, Thorsten and Li, Nuo and Ondřej, Rypáček (2014) Some constructions on ω-groupoids. In: International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP '14), 17 Jul 2014, Vienna, Austria.
Official URL: http://dl.acm.org/citation.cfm?doid=2631172.2631176
Weak ω-groupoids are the higher dimensional generalisation of setoids and are an essential ingredient of the construc- tive semantics of Homotopy Type Theory . Following up on our previous formalisation  and Brunerie’s notes , we present a new formalisation of the syntax of weak ω- groupoids in Agda using heterogeneous equality. We show how to recover basic constructions on ω-groupoids using sus- pension and replacement. In particular we show that any type forms a groupoid and we outline how to derive higher dimensional composition. We present a possible semantics using globular sets and discuss the issues which arise when using globular types instead.
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