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 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 language | English (US) |
|---|---|
| Article number | 35 |
| Pages (from-to) | 1213-1221 |
| Number of pages | 9 |
| Journal | Theory and Applications of Categories |
| Volume | 32 |
| State | Published - 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.
Keywords
- Enriched localization
- Invertibility hypothesis