Gambino, N orcid.org/0000-0002-4257-3590 and Larrea, MF (2021) Models of Martin-Löf Type Theory from Algebraic Weak Factorisation Systems. The Journal of Symbolic Logic. 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 to 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.
Metadata
Authors/Creators: |
|
||||
---|---|---|---|---|---|
Copyright, Publisher and Additional Information: | © The Association for Symbolic Logic 2021.This article has been published in a revised form in The Journal of Symbolic Logic https://doi.org/10.1017/jsl.2021.39. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. | ||||
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: | 27 Apr 2021 08:46 | ||||
Last Modified: | 21 Aug 2021 01:51 | ||||
Status: | Published online | ||||
Publisher: | Cambridge University Press | ||||
Identification Number: | https://doi.org/10.1017/jsl.2021.39 |