Functors between Reedy model categories of diagrams

Abstract

If $D$ is a Reedy category and $M$ is a model category, the category $M^D$ of $D$-diagrams in $M$ is a model category under the Reedy model category structure. If $C\to D$ is a Reedy functor between Reedy categories, then there is an induced functor of diagram categories $M^D\to M^C$. Our main result is a characterization of the Reedy functors $C\to D$ that induce right or left Quillen functors $M^D\to M^C$ for every model category $M$. We apply these results to various situations, and in particular show that certain important subdiagrams of a fibrant multicosimplicial object are fibrant.

arXiv comment38 pages, final version

References in corpus (1)

• The diagonal of a multicosimplicial object

Cited by in corpus (1)

• A graphical category for higher modular operads