Functors between Reedy model categories of diagrams
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 \(C → D\) is a Reedy functor between Reedy categories, then there is an induced functor of diagram categories \(M^D → M^C \). Our main result is a characterization of the Reedy functors \(C → D\) that induce right or left Quillen functors \(M^D → M^C \) 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., number=5, journal=North-Western European Journal of Mathematics, author=Hirschhorn , Philip S. and Volić , Ismar, year=2019, month=Apr., pages=21–68