Gambino, N orcid.org/0000-0002-4257-3590 and Henry, S (2022) Towards a constructive simplicial model of Univalent Foundations. Journal of the London Mathematical Society, 105 (2). pp. 1073-1109. ISSN 0024-6107
Abstract
We provide a partial solution to the problem of defining a constructive version of Voevodsky's simplicial model of Univalent Foundations. For this, we prove constructive counterparts of the necessary results of simplicial homotopy theory, building on the constructive version of the Kan-Quillen model structure established by the second-named author. In particular, we show that dependent products along fibrations with cofibrant domains preserve fibrations, establish the weak equivalence extension property for weak equivalences between fibrations with cofibrant domain and define a univalent fibration that classifies small fibrations between bifibrant objects. These results allow us to define a comprehension category supporting identity types, Σ-types, ∏-types and a univalent universe, leaving only a coherence question to be addressed.
Metadata
Authors/Creators: |
|
||||||
---|---|---|---|---|---|---|---|
Copyright, Publisher and Additional Information: | © 2022 The Authors.This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. | ||||||
Dates: |
|
||||||
Institution: | The University of Leeds | ||||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||||
Funding Information: |
|
||||||
Depositing User: | Symplectic Publications | ||||||
Date Deposited: | 05 Aug 2021 11:56 | ||||||
Last Modified: | 08 May 2023 19:10 | ||||||
Status: | Published | ||||||
Publisher: | Wiley | ||||||
Identification Number: | https://doi.org/10.1112/jlms.12532 |