Title: The univalence axiom in cubical sets,
Abstract: In this note we show that Voevodsky's univalence axiom holds in the model of
type theory based on symmetric cubical sets. We will also discuss Swan's
construction of the identity type in this variation of cubical sets. This
proves that we have a model of type theory supporting dependent products,
dependent sums, univalent universes, and identity types with the usual
judgmental equality, and this model is formulated in a constructive metatheory.