Monoidal Relative Categories Model Monoidal $\infty$-Categories
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917363334512640 |
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| author | Arakawa, Kensuke |
| author_facet | Arakawa, Kensuke |
| contents | We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal $\infty$-categories, and likewise in the symmetric monoidal setting. As an application, we give a concise and complete proof of the fact that every presentably monoidal or presentably symmetric monoidal $\infty$-category is presented by a monoidal or symmetric monoidal model category, which, in the monoidal case, was sketched by Lurie, and in the symmetric monoidal case, was proved by Nikolaus--Sagave. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monoidal Relative Categories Model Monoidal $\infty$-Categories Arakawa, Kensuke Category Theory Algebraic Topology We prove that the homotopy theory of monoidal relative categories is equivalent to that of monoidal $\infty$-categories, and likewise in the symmetric monoidal setting. As an application, we give a concise and complete proof of the fact that every presentably monoidal or presentably symmetric monoidal $\infty$-category is presented by a monoidal or symmetric monoidal model category, which, in the monoidal case, was sketched by Lurie, and in the symmetric monoidal case, was proved by Nikolaus--Sagave. |
| title | Monoidal Relative Categories Model Monoidal $\infty$-Categories |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2504.20606 |