Enriched model categories and the Dold-Kan correspondence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918491433467904 |
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| author | Frankland, Martin Ngompé, Arnaud Ngopnang |
| author_facet | Frankland, Martin Ngompé, Arnaud Ngopnang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_14291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enriched model categories and the Dold-Kan correspondence Frankland, Martin Ngompé, Arnaud Ngopnang Algebraic Topology Category Theory 55U35 (Primary) 18N40, 18D20, 18M05, 18G31 (Secondary) 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. |
| title | Enriched model categories and the Dold-Kan correspondence |
| topic | Algebraic Topology Category Theory 55U35 (Primary) 18N40, 18D20, 18M05, 18G31 (Secondary) |
| url | https://arxiv.org/abs/2508.14291 |