Parametrized stability and the universal property of global spectra

We develop a framework of parametrized semiadditivity and stability with respect to so‐called atomic orbital subcategories of an indexing ‐category , extending work of Nardin. Specializing this framework, we introduce global ‐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 ‐category with a natural global ‐category of global spectra for finite groups, in the sense of Schwede and Hausmann.