Linskens, Sil and Nardin, Denis and Pol, Luca (2025) Global homotopy theory via partially lax limits. GEOMETRY & TOPOLOGY, 29 (3). pp. 1345-1440. ISSN 1465-3060, 1364-0380
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We provide new oc-categorical models for unstable and stable global homotopy theory. We use the notion of partially lax limits to formalize the idea that a global object is a collection of G-objects, one for each compact Lie group G, which are compatible with the restriction-inflation functors. More precisely, we show that the oc-category of global spaces is equivalent to a partially lax limit of the functor sending a compact Lie group G to the oc-category of G-spaces. We also prove the stable version of this result, showing that the oc-category of global spectra is equivalent to the partially lax limit of a diagram of G-spectra. Finally, the techniques employed in the previous cases allow us to describe the oc-category of proper G-spectra for a Lie group G, as a limit of a diagram of H-spectra for H running over all compact subgroups of G.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EQUIVARIANT; LOCALIZATION; ALGEBRAS |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 May 2026 08:21 |
| Last Modified: | 07 May 2026 08:21 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65818 |
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