The Univalence Axiom in posetal model categories

Assaf Hasson, Itay Kaplan

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)669-682
Number of pages14
JournalJournal of Logic and Computation
Volume25
Issue number3
DOIs
StatePublished - 1 Jun 2015

Keywords

  • Posetal model categories
  • set theory
  • univalence axiom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Arts and Humanities (miscellaneous)
  • Hardware and Architecture
  • Logic

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