Enriched model categories and the Dold-Kan correspondence

The monoidal properties of the Dold-Kan correspondence have been studied in homotopy theory, notably by Schwede and Shipley. Changing the enrichment of an enriched, tensored, and cotensored category along the Dold-Kan correspondence does not preserve the tensoring nor the cotensoring. More generally, what happens to an enriched model category if we change the enrichment along a weak monoidal Quillen pair? We prove a change of base theorem that describes which properties are preserved and which are weakened. We also provide sources of examples of weak monoidal Quillen pairs, including in equivariant homotopy theory.