Year: 2025
Type: article
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 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 G -category of genuine G G -spectra for any finite group G G , previously formulated by Nardin [ Stability and distributivity over orbital infinity-categories , ProQuest LLC, Ann Arbor, MI, 2017, Thesis (Ph.D.)-Massachusetts Institute of Technology].
DOI: 10.1090/tran/9497
Authors: Bastiaan Cnossen, Tobias Lenz, Sil Linskens
Institutions: University of Bonn, University of Regensburg, Utrecht University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4412483590