Enriched model categories and the Dold-Kan correspondence

Martin Frankland; Arnaud Ngopnang Ngompé

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arXiv · 2508.14291

Enriched model categories and the Dold-Kan correspondence

Martin Frankland·Arnaud Ngopnang Ngompé

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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.

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BibTeX RIS

Martin Frankland, Arnaud Ngopnang Ngompé. 2025-08-19. Enriched model categories and the Dold-Kan correspondence. https://arxiv.org/abs/2508.14291

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