On the equivalence of two approaches to multiplicative homotopy theories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911547189624832 |
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| author | Arakawa, Kensuke |
| author_facet | Arakawa, Kensuke |
| contents | We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their homotopy theories.
As consequences, we solve Pavlov's conjecture and obtain a solution to a special case of Hovey's 10th problem. We also prove several variations of the main theorem, such as an analog for non-symmetric monoidal semi-model categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23018 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the equivalence of two approaches to multiplicative homotopy theories Arakawa, Kensuke Category Theory Algebraic Topology We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their homotopy theories. As consequences, we solve Pavlov's conjecture and obtain a solution to a special case of Hovey's 10th problem. We also prove several variations of the main theorem, such as an analog for non-symmetric monoidal semi-model categories. |
| title | On the equivalence of two approaches to multiplicative homotopy theories |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2603.23018 |