Parameterized stability and the universal property of global spectra

Abstract

Extending work of Nardin, we develop a framework of parameterized semiadditivity and stability with respect to so-called atomic orbital subcategories of an indexing $\infty$-category $T$. Specializing this framework, we introduce global $\infty$-categories together with genuine forms of 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 genuinely stable global $\infty$-category with a natural global $\infty$-category of global spectra for finite groups, in the sense of Schwede and Hausmann.