English

The univalence axiom in posetal model categories

Category Theory 2011-11-16 v1

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 QtQt in which the mapping Hom(w)(Z×B,C):QtSetsHom^{(w)}(Z\times B,C):Qt\longrightarrow Sets is functorial in ZZ and represented in QtQt 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.

Keywords

Cite

@article{arxiv.1111.3489,
  title  = {The univalence axiom in posetal model categories},
  author = {Misha Gavrilovich and Assaf Hasson and Itay Kaplan},
  journal= {arXiv preprint arXiv:1111.3489},
  year   = {2011}
}