  We construct a univalent universe in the sense of Voevodsky in some suitable
model categories for homotopy types (obtained from Grothendieck's theory of
test categories). In practice, this means for instance that, appart from the
homotopy theory of simplicial sets, intensional type theory with the univalent
axiom can be interpreted in the homotopy theory of cubical sets (with
connections or not), or of Joyal's cellular sets.
