• A
• A
• A
• ABC
• ABC
• ABC
• А
• А
• А
• А
• А
Regular version of the site

## The Univalence Axiom in posetal model categories.

Journal of Logic and Computation. 2015. Vol. 25. No. 3. P. 669-682.
Gavrilovich M., Hasson A., Kaplan I.

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 in Qt
satis es our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work
was motivated by a question reported in [Gar11], asking for a model of the Univalence Axiom not
equivalent to the standard one.