The univalence axiom in posetal model categories
Category Theory
2011-11-16 v1
Abstract
In this note we interpret Voevodsky's Univalence Axiom in the language of (abstract) model categories. We then show that any posetal locally Cartesian closed model category in which the mapping is functorial in and represented in satisfies our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work was motivated by a question reported in [Ob], asking for a model of the Univalence Axiom not equivalent to the standard one.
Keywords
Cite
@article{arxiv.1111.3489,
title = {The univalence axiom in posetal model categories},
author = {Misha Gavrilovich and Assaf Hasson and Itay Kaplan},
journal= {arXiv preprint arXiv:1111.3489},
year = {2011}
}