Enriched model categories and the Dold-Kan correspondence

TL;DR

This paper investigates how changing enrichment along weak monoidal Quillen pairs affects the structure of enriched model categories, providing a change of base theorem and examples in equivariant homotopy theory.

Contribution

It establishes a change of base theorem for enriched model categories along weak monoidal Quillen pairs and explores implications in homotopy theory.

Findings

Change of base theorem describes property preservation in enriched model categories.

Examples of weak monoidal Quillen pairs are provided, including in equivariant homotopy theory.

Changing enrichment can weaken tensoring and cotensoring properties.

Abstract

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.