Dualizable presentable $\infty$-categories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912090803929088 |
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| author | Ramzi, Maxime |
| author_facet | Ramzi, Maxime |
| contents | We prove that for any presentably symmetric monoidal $\infty$-category $\mathcal{V}$, the $\infty$-category $\mathbf{Mod}_\mathcal{V}(\mathbf{Pr}^{\mathrm{L}})^{\mathrm{dbl}}$ of dualizable presentable $\mathcal{V}$-modules and internal left adjoints between them is itself presentable.
Along the way, we survey formal properties of these dualizable $\mathcal V$-modules. We pay close attention to the case of the $\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dualizable presentable $\infty$-categories Ramzi, Maxime Category Theory Algebraic Topology K-Theory and Homology We prove that for any presentably symmetric monoidal $\infty$-category $\mathcal{V}$, the $\infty$-category $\mathbf{Mod}_\mathcal{V}(\mathbf{Pr}^{\mathrm{L}})^{\mathrm{dbl}}$ of dualizable presentable $\mathcal{V}$-modules and internal left adjoints between them is itself presentable. Along the way, we survey formal properties of these dualizable $\mathcal V$-modules. We pay close attention to the case of the $\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''. |
| title | Dualizable presentable $\infty$-categories |
| topic | Category Theory Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2410.21537 |