Parameterized stability and the universal property of global spectra

Bastiaan Cnossen, Tobias Lenz, Sil Linskens

Research output: Working paperPreprintAcademic

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.
Original languageEnglish
PublisherarXiv
Pages1-103
Number of pages103
DOIs
Publication statusPublished - 19 Jan 2023

Bibliographical note

103 pages

Keywords

  • math.AT
  • 55U35, 55P91 (Primary)

Fingerprint

Dive into the research topics of 'Parameterized stability and the universal property of global spectra'. Together they form a unique fingerprint.

Cite this