Year: 2025
Type: article
Abstract: We provide new 1-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 1-category of global spaces is equivalent to a partially lax limit of the functor sending a compact Lie group G to the 1-category of G-spaces.We also prove the stable version of this result, showing that the 1-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 1-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. 55N91, 55P91; 18N70 1. Introduction 1346 I. Partially lax limits, promonoidal 1-categories and Day convolution 1355 2. From topological/model categories to 1-categories 1355 3. Promonoidal 1-categories and Day convolution 1360 4. Partially lax limits 1372 5. Partially lax limits of symmetric monoidal 1-categories 1377 II.1-categories of global objects as partially lax limits 1382 6. Global spaces as a partially lax limit 1382 7. 1-categories of equivariant prespectra 1390 8. Models for 1-categories of equivariant prespectra 1401 9. Functoriality of equivariant prespectra 1408 10.Functoriality of equivariant spectra 1418 11.Global spectra as a partially lax limit 1424 12. Proper equivariant spectra as a limit 1430 Appendix.Tensor product of modules in an 1-category 1433
Source: Geometry & Topology
Authors: Sil Linskens, Denis Nardin, Luca Pol
Institution: University of Regensburg
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411053755