Functors between Reedy model categories of diagrams

2015/11/16 by Philip Hirschhorn, Hirschhorn, Philip S., Ismar Volić +1
Computer Science · Mathematics · #18G55 #55U35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Computer science #FOS: Mathematics #Functor #Homotopy and Cohomology in Algebraic Topology #Mathematics #Programming language #Pure mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1511.04809

openalex publication_date 2015/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 → 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.

Citations

• The diagonal of a multicosimplicial object

Related

• On Reedy Model Categories
• Reedy categories and their generalizations
• Enriched Reedy categories
• Reedy diagrams in symmetric monoidal model categories
• On modified Reedy and modified projective model structures