Gambino, N orcid.org/0000-0002-4257-3590 and Larrea, MF (2023) Models of Martin-Löf Type Theory from Algebraic Weak Factorisation Systems. The Journal of Symbolic Logic, 88 (1). pp. 242-289. ISSN 0022-4812
Abstract
We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-Löf type theory. This is done by showing that the comprehension category associated with a type-theoretic algebraic weak factorisation system satisfies the assumptions necessary to apply a right adjoint method for splitting comprehension categories. We then provide methods for constructing several examples of type-theoretic algebraic weak factorisation systems, encompassing the existing groupoid and cubical sets models, as well as new models based on normal fibrations.
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Copyright, Publisher and Additional Information: | © The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||||
Keywords: | Martin-Löf theory; comprehension category; algebraic weak factorisation system | ||||
Dates: |
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 27 Apr 2021 08:46 | ||||
Last Modified: | 23 Mar 2023 18:49 | ||||
Status: | Published | ||||
Publisher: | Cambridge University Press | ||||
Identification Number: | https://doi.org/10.1017/jsl.2021.39 |