arXiv Open Access 2023

Classification of fully dualizable linear categories

Germán Stefanich

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Abstrak

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.

Topik & Kata Kunci

math.CT math.AG math.AT

Penulis (1)

Germán Stefanich

Format Sitasi

APA MLA BibTeX

Stefanich, G. (2023). Classification of fully dualizable linear categories. https://arxiv.org/abs/2307.16337

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓