Abstract
Parsummable categories were introduced by Schwede as input for his global algebraic K-theory construction. We prove that their whole homotopy theory with respect to the so-called global equivalences can already be modelled by the more mundane symmetric monoidal categories. In another direction, we show that the resulting homotopy theory is also equivalent to the homotopy theory of a certain simplicial analogue of parsummable categories, that we call parsummable simplicial sets. These form a bridge to several concepts of ‘globally coherently commutative monoids’ like ultra-commutative monoids and global -spaces, that we explore in.
| Original language | English |
|---|---|
| Pages (from-to) | 635-686 |
| Number of pages | 52 |
| Journal | New York Journal of Mathematics |
| Volume | 29 |
| Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:© 2023, University at Albany. All rights reserved.
Funding
I am grateful to the Max Planck Institute for Mathematics in Bonn for their hospitality and support during my PhD studies. At the time the first version of this article was written, I was an associate member of the Hausdorff Center for Mathematics, funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy (GZ 2047/1, project ID 390685813).
| Funders | Funder number |
|---|---|
| Deutsche Forschungsgemeinschaft | 390685813, GZ 2047/1 |
| Hausdorff Center for Mathematics |
Keywords
- G-global homotopy theory
- Symmetric monoidal categories
- equivariant algebraic K-theory
- global homotopy theory
- parsummable categories