Localization of enriched categories and cubical sets

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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 CatS 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.

Original languageEnglish (US)
Article number35
Pages (from-to)1213-1221
Number of pages9
JournalTheory and Applications of Categories
StatePublished - Sep 8 2017

Bibliographical note

Funding Information:
Partially supported by NSF grant DMS–1206008. Received by the editors 2016-02-22 and, in final form, 2017-08-09. Transmitted by Ieke Moerdijk. Published on 2017-09-08. 2010 Mathematics Subject Classification: 18D20 (primary) 18G55, 18E35 (secondary). Key words and phrases: Enriched localization, invertibility hypothesis. ©c Tyler Lawson, 2017. Permission to copy for private use granted.


  • Enriched localization
  • Invertibility hypothesis

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