  The invertibility hypothesis for a monoidal model category S asks that
localizing an S-enriched category with respect to an equivalence results in an
weakly equivalent enriched category. This is the most technical among the
axioms for S to be an excellent model category in the sense of Lurie, who
showed that the category of S-enriched categories then has a model structure
with characterizable fibrant objects. We use a universal property of cubical
sets, as a monoidal model category, to show that the invertibility hypothesis
is consequence of the other axioms.
