Reedy Diagrams in V-Model Categories

摘要

We study the category of Reedy diagrams in a V-model category. Explicitly, we show that if K is a small category, V is a closed symmetric monoidal category and C is a closed V-module, then the diagram category VK is a closed symmetric monoidal category and the diagram category CK is a closed VK-module. We then prove that if further K is a Reedy category, Vis a monoidal model category and C is a V-model category, then with the Reedy model category structures, VKis a monoidal model category and CK is a VK-model category provided that either the unit 1 of V is cofibrant or V is cofibrantly generated.