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.

arXiv commentv3: minor revision following a referee report. Accepted for publication in J. Topol., 112 pages

References in corpus (13)

• Global homotopy theory
• Diagram spaces and symmetric spectra
• Parametrized higher category theory
• Global orthogonal spectra
• Mackey 2-functors and Mackey 2-motives
• Symmetric spectra model global homotopy theory of finite groups
• Orbispaces, orthogonal spaces, and the universal compact Lie group
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• Global homotopy theory via partially lax limits
• Operads in Unstable Global Homotopy Theory
• Orbifold bordism and duality for finite orbispectra
• Global transfer systems of abelian compact Lie groups
• Genuine vs. naïve symmetric monoidal G-categories