Parametrized stability and the universal property of global spectra
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914177823539200 |
|---|---|
| author | Cnossen, Bastiaan Lenz, Tobias Linskens, Sil |
| author_facet | Cnossen, Bastiaan Lenz, Tobias Linskens, Sil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08240 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parametrized stability and the universal property of global spectra Cnossen, Bastiaan Lenz, Tobias Linskens, Sil Algebraic Topology 55U35, 55P91 (Primary) 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. |
| title | Parametrized stability and the universal property of global spectra |
| topic | Algebraic Topology 55U35, 55P91 (Primary) |
| url | https://arxiv.org/abs/2301.08240 |