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 (Formula presented.) -category (Formula presented.), extending work of Nardin. Specializing this framework, we introduce global (Formula presented.) -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 (Formula presented.) -category with a natural global (Formula presented.) -category of global spectra for finite groups, in the sense of Schwede and Hausmann.