Parametrized stability and the universal property of global spectra

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.