Localization of enriched categories and cubical sets

TL;DR

This paper demonstrates that the invertibility hypothesis for a monoidal model category of cubical sets follows from other axioms, simplifying the criteria for an excellent model category as defined by Lurie.

Contribution

It proves that the invertibility hypothesis is a consequence of other axioms in the context of cubical sets, reducing the complexity of establishing an excellent model category.

Findings

Invertibility hypothesis follows from other axioms in cubical sets

Simplifies criteria for Lurie's excellent model categories

Uses universal property of cubical sets

Abstract

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.