(joint work with J. Weinberger)

Abstract: Voevodsky's model of the Univalence Axion in simplicial sets is not constructive as shown by Coquand et al. To avoid this problem Cohen, Coquand, Huber, Moertberg have constructed in Cubical Sets a model of a Cubical Type Theory which has computational meaning.

We show that simplicial sets form a subtopos of cubical sets which allows one to contructively reason in the latter about the former.