Some constructions on ω-groupoids

Altenkirch, Thorsten, 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.

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Weak ω-groupoids are the higher dimensional generalisation of setoids and are an essential ingredient of the construc- tive semantics of Homotopy Type Theory [10]. Following up on our previous formalisation [3] and Brunerie’s notes [5], 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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published in: LFMTP 2014: proceedings of the Ninth International Workshop on Logical Frameworks and Meta-Languages: Theory & Practice: July 17, 2014, Vienna, Austria. New York : Association for Computing Machinery, 2014, ISBN: 978-1-4503-2817-3. Article no. 4, doi: 10.1145/2631172.2631176
Keywords: Logic Programming, Groupoids
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
Depositing User: Altenkirch, Thorsten
Date Deposited: 15 Mar 2015 15:42
Last Modified: 04 May 2020 20:16

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