Induced model structures for higher categories

Hackney, Philip; Rovelli, Martina

doi:10.1090/proc/15982

Induced model structures for higher categories
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by Philip Hackney and Martina Rovelli PDF

Proc. Amer. Math. Soc. 150 (2022), 4629-4644

Abstract:

We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an application, we construct new model structures on cubical sets, prederivators, marked simplicial sets and simplicial spaces modeling $\infty$-categories and $\infty$-groupoids.

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