Classification of fully dualizable linear categories
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916636830728192 |
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| author | Stefanich, Germán |
| author_facet | Stefanich, Germán |
| contents | We prove that if $R$ is a G-ring then every fully dualizable $R$-linear cocomplete category is equivalent to a twist by a $\mathbb{G}_m$-gerbe of the category of modules over a finite étale $R$-algebra. We also show that this holds more generally over an arbitrary commutative ring under an additional compact generation hypothesis. We include variants of these results that apply to $R$-linear graded categories, and to the context of $\infty$-categories linear over connective commutative ring spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16337 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of fully dualizable linear categories Stefanich, Germán Category Theory Algebraic Geometry Algebraic Topology We prove that if $R$ is a G-ring then every fully dualizable $R$-linear cocomplete category is equivalent to a twist by a $\mathbb{G}_m$-gerbe of the category of modules over a finite étale $R$-algebra. We also show that this holds more generally over an arbitrary commutative ring under an additional compact generation hypothesis. We include variants of these results that apply to $R$-linear graded categories, and to the context of $\infty$-categories linear over connective commutative ring spectra. |
| title | Classification of fully dualizable linear categories |
| topic | Category Theory Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2307.16337 |