Reedy diagrams in symmetric monoidal model categories

2016/09/30 by Moncef Ghazel, Ghazel, Moncef, Fethi Kadhi +1
Mathematics · Physics and Astronomy · #18D10 #18D15 #19D23 #55U35 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1609.09623

openalex publication_date 2016/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a small category I and a closed symmetric monoidal category \mm, we show that the diagram category \mm^I with the objectwise product is a closed symmetric monoidal category. We then prove that if I is a Reedy category and \mm has a model structure compatible with its product, then so is the Reedy model structure on \mm^I provided that \mm is cofibrantly generated.

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• Monoidal model categories
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