Norms in equivariant homotopy theory
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911502353563648 |
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| author | Lenz, Tobias Linskens, Sil Pützstück, Phil |
| author_facet | Lenz, Tobias Linskens, Sil Pützstück, Phil |
| contents | We show that the $\infty$-category of normed algebras in genuine $G$-spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in $G$-symmetric spectra for any finite group $G$. We moreover provide an analogous description of Schwede's ultra-commutative global ring spectra in higher categorical terms.
Using these new descriptions, we exhibit the $\infty$-category of ultra-commutative global ring spectra as a partially lax limit of the $\infty$-categories of genuine $G$-spectra for varying $G$, in analogy with the non-multiplicative comparison of Nardin, Pol, and the second author.
Along the way, we establish various new results in parametrized higher algebra, which we hope to be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Norms in equivariant homotopy theory Lenz, Tobias Linskens, Sil Pützstück, Phil Algebraic Topology Category Theory 18N70, 55P91, 55P43 (Primary), 18N60 (Secondary) We show that the $\infty$-category of normed algebras in genuine $G$-spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in $G$-symmetric spectra for any finite group $G$. We moreover provide an analogous description of Schwede's ultra-commutative global ring spectra in higher categorical terms. Using these new descriptions, we exhibit the $\infty$-category of ultra-commutative global ring spectra as a partially lax limit of the $\infty$-categories of genuine $G$-spectra for varying $G$, in analogy with the non-multiplicative comparison of Nardin, Pol, and the second author. Along the way, we establish various new results in parametrized higher algebra, which we hope to be of independent interest. |
| title | Norms in equivariant homotopy theory |
| topic | Algebraic Topology Category Theory 18N70, 55P91, 55P43 (Primary), 18N60 (Secondary) |
| url | https://arxiv.org/abs/2503.02839 |