Induced model structures for higher categories

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.

15 pages, to appear in Proc. Amer. Math. Soc

References in corpus (2)

• Cubical models of $(\infty ,1)$-categories
• Joyal's cylinder conjecture

Cited by in corpus (1)

• Relative elegance and cartesian cubes with one connection