%0 Journal Article
%T The univalence axiom in posetal model categories
%A Misha Gavrilovich
%A Assaf Hasson
%A Itay Kaplan
%J Mathematics
%D 2011
%I arXiv
%X 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 $Hom^{(w)}(Z\times B,C):Qt\longrightarrow Sets$ is functorial in $Z$ and represented in $Qt$ 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.
%U http://arxiv.org/abs/1111.3489v1