Cnossen, Bastiaan and Lenz, Tobias and Linskens, Sil (2025) Partial parametrized presentability and the universal property of equivariant spectra. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 378 (10). pp. 6913-6974. ISSN 0002-9947, 1088-6850
Full text not available from this repository.Abstract
. 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 Cnossen, Lenz, and Linskens [Parametrized stability and the universal property of global spectra, 2023]. 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 Cnossen, Lenz, and Linskens [Parametrized stability and the universal property of global spectra, 2023], 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 [Stability and distributivity (Ph.D.)-Massachusetts Institute of Technology].
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GLOBAL HOMOTOPY-THEORY |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 12 Aug 2026 05:49 |
| Last Modified: | 12 Aug 2026 05:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67036 |
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