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arXiv · 2301.08240

Parametrized stability and the universal property of global spectra

Bastiaan Cnossen·Tobias Lenz·Sil Linskens
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Abstract

We develop a framework of parametrized semiadditivity and stability with respect to so-called atomic orbital subcategories of an indexing $\infty$-category $T$, extending work of Nardin. Specializing this framework, we introduce global $\infty$-categories and the notions of equivariant semiadditivity and stability, yielding a higher categorical version of the notion of a Mackey 2-functor studied by Balmer-Dell'Ambrogio. As our main result, we identify the free presentable equivariantly stable global $\infty$-category with a natural global $\infty$-category of global spectra for finite groups, in the sense of Schwede and Hausmann.

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Bastiaan Cnossen, Tobias Lenz, Sil Linskens. 2025-09-17. Parametrized stability and the universal property of global spectra. https://doi.org/10.1112/topo.70044

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