Geodesic
Localization of enriched categories and cubical sets
Theory and applications of categories, Tome 32 (2017), pp. 1213-1221

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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 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.

Publié le :
Classification : 18D20 (primary) 18G55, 18E35 (secondary)
Keywords: Enriched localization, invertibility hypothesis 
@article{TAC_2017_32_a34,
     author = {Tyler Lawson},
     title = {Localization of enriched categories and cubical sets},
     journal = {Theory and applications of categories},
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     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a34/}
}
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Tyler Lawson. Localization of enriched categories and cubical sets. Theory and applications of categories, Tome 32 (2017), pp. 1213-1221. http://geodesic.mathdoc.fr/item/TAC_2017_32_a34/