Gambino, N orcid.org/0000-0002-4257-3590 and Sattler, C (2017) The Frobenius condition, right properness, and uniform fibrations. Journal of Pure and Applied Algebra, 221 (12). pp. 3027-3068. ISSN 0022-4049
Abstract
We develop further the theory of weak factorization systems and algebraic weak factorization systems. In particular, we give a method for constructing (algebraic) weak factorization systems whose right maps can be thought of as (uniform) fibrations and that satisfy the (functorial) Frobenius condition. As applications, we obtain a new proof that the Quillen model structure for Kan complexes is right proper, avoiding entirely the use of topological realization and minimal fibrations, and we solve an open problem in the study of Voevodsky's simplicial model of type theory, proving a constructive version of the preservation of Kan fibrations by pushforward along Kan fibrations. Our results also subsume and extend work by Coquand and others on cubical sets.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY). |
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: | Funder Grant number John Templeton Foundation - DO NOT USE 48138 Air Force Research Lab Munitions Directorate FA8655-13-1-3038, 12.800 EPSRC EP/M01729X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Feb 2017 11:08 |
Last Modified: | 17 Jan 2018 01:31 |
Published Version: | https://doi.org/10.1016/j.jpaa.2017.02.013 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jpaa.2017.02.013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111801 |