Partial parametrized presentability and the universal property of equivariant spectra
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918143107006464 |
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| author | Cnossen, Bastiaan Lenz, Tobias Linskens, Sil |
| author_facet | Cnossen, Bastiaan Lenz, Tobias Linskens, Sil |
| contents | We introduce a notion of partial presentability in parametrized higher category theory and investigate its interaction with the concepts of parametrized semiadditivity and stability from arXiv:2301.08240. In particular, we construct the free partially presentable $T$-categories in the unstable, semiadditive, and stable contexts and explain how to exhibit them as full subcategories of their fully presentable analogues.
Specializing our results to the setting of (global) equivariant homotopy theory, we obtain a notion of equivariant presentability for the global categories of arXiv:2301.08240, and we show that the global category of genuine equivariant spectra is the free global category that is both equivariantly presentable and equivariantly stable. As a consequence, we deduce the analogous result about the $G$-category of genuine $G$-spectra for any finite group $G$, previously formulated by Nardin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11001 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Partial parametrized presentability and the universal property of equivariant spectra Cnossen, Bastiaan Lenz, Tobias Linskens, Sil Algebraic Topology 55U35, 55P91 (Primary) We introduce a notion of partial presentability in parametrized higher category theory and investigate its interaction with the concepts of parametrized semiadditivity and stability from arXiv:2301.08240. In particular, we construct the free partially presentable $T$-categories in the unstable, semiadditive, and stable contexts and explain how to exhibit them as full subcategories of their fully presentable analogues. Specializing our results to the setting of (global) equivariant homotopy theory, we obtain a notion of equivariant presentability for the global categories of arXiv:2301.08240, and we show that the global category of genuine equivariant spectra is the free global category that is both equivariantly presentable and equivariantly stable. As a consequence, we deduce the analogous result about the $G$-category of genuine $G$-spectra for any finite group $G$, previously formulated by Nardin. |
| title | Partial parametrized presentability and the universal property of equivariant spectra |
| topic | Algebraic Topology 55U35, 55P91 (Primary) |
| url | https://arxiv.org/abs/2307.11001 |