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 Cat_S 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 a consequence of the other axioms.
Keywords: Enriched localization, invertibility hypothesis
2010 MSC: 18D20 (primary) 18G55, 18E35 (secondary)
Theory and Applications of Categories, Vol. 32, 2017, No. 35, pp 1213-1221.