  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.
