2011/11/15 by Gavrilovich, Misha, Hasson, Assaf, Kaplan, Itay
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1111.3489
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\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.