Free higher groups in homotopy type theory

Kraus, Nicolai and Altenkirch, Thorsten (2018) Free higher groups in homotopy type theory. In: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 9–12 July 2018, Oxford, England.

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Given a type A in homotopy type theory (HoTT), we can define the free ∞-group on A as the higher inductive type F (A)with constructors unit: F(A),cons : A → F(A) → F(A), and conditions saying that every cons(a)is an auto-equivalence on F(A). Equivalently, we can take the loop space of the suspension of A + 1. Assuming that A is a set (i.e. satisfies the principle of unique identity proofs), we are interested in the question whether F(A) is a set as well, which is very much related to an open problem in the HoTT book [20, Ex. 8.2]. We show an approximation to the question, namely that the fundamental groups of F(A) are trivial, i.e. that ∥F(A)∥1 is a set.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Published in: LICS '18 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, ISBN: 978-1-4503-5583-4 ; doi:10.1145/3209108.3209183
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
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Depositing User: Altenkirch, Thorsten
Date Deposited: 18 Apr 2018 11:10
Last Modified: 20 Sep 2018 10:13

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