Rigidification of connective comodules
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916196569317376 |
|---|---|
| author | Péroux, Maximilien |
| author_facet | Péroux, Maximilien |
| contents | Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of homotopy coherent comodules is represented by a model category of strict comodules in non-negative chain complexes over $\mathbb{k}$. These comodules are over a coalgebra that is strictly coassociative and simply connected. The rigidification result allows us to derive the notion of cotensor product of comodules and endows the $\infty$-category of comodules with a symmetric monoidal structure via the two-sided cobar resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_09398 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rigidification of connective comodules Péroux, Maximilien Algebraic Topology Category Theory 18N40, 18N70, 55P43 (Primary) 16T15, 55U15 (Secondary) Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of homotopy coherent comodules is represented by a model category of strict comodules in non-negative chain complexes over $\mathbb{k}$. These comodules are over a coalgebra that is strictly coassociative and simply connected. The rigidification result allows us to derive the notion of cotensor product of comodules and endows the $\infty$-category of comodules with a symmetric monoidal structure via the two-sided cobar resolution. |
| title | Rigidification of connective comodules |
| topic | Algebraic Topology Category Theory 18N40, 18N70, 55P43 (Primary) 16T15, 55U15 (Secondary) |
| url | https://arxiv.org/abs/2006.09398 |