Group completion via the action $\infty$-category
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911882275717120 |
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| author | Lehner, Georg |
| author_facet | Lehner, Georg |
| contents | We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary $E_n$-monoids as an $E_{n-1}$-monoidal $\infty$-category and show that its realization models the group completion provided that $n \geq 2$. We will also show how this construction is related to a variety of other constructions of the group completion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Group completion via the action $\infty$-category Lehner, Georg K-Theory and Homology Category Theory 19D06 (Primary), 19D23, 18N60, 18N70 (Secondary) We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary $E_n$-monoids as an $E_{n-1}$-monoidal $\infty$-category and show that its realization models the group completion provided that $n \geq 2$. We will also show how this construction is related to a variety of other constructions of the group completion. |
| title | Group completion via the action $\infty$-category |
| topic | K-Theory and Homology Category Theory 19D06 (Primary), 19D23, 18N60, 18N70 (Secondary) |
| url | https://arxiv.org/abs/2405.12118 |