The Univalence Axiom in posetal model categories

Assaf Hasson; Itay Kaplan

doi:10.1093/logcom/exu022

The Univalence Axiom in posetal model categories

Assaf Hasson, Itay Kaplan

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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 Qt in which the mapping Hom(w)(Z×B,C):Qt→Sets is functorial in Z and represented inQt satisfies our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work was motivated by a question reported in [2], asking for a model of the Univalence Axiom not equivalent to the standard one.

Original language	American English
Pages (from-to)	669-682
Number of pages	14
Journal	Journal of Logic and Computation
Volume	25
Issue number	3
DOIs	https://doi.org/10.1093/logcom/exu022
State	Published - 1 Jun 2015

Bibliographical note

Publisher Copyright:
© 2015 The Author.

Keywords

Posetal model categories
set theory
univalence axiom

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10.1093/logcom/exu022

Cite this

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The Univalence Axiom in posetal model categories

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