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Classification of fully dualizable linear categories

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arxiv 2307.16337 v2 pith:5VFFVUE7 submitted 2023-07-30 math.CT math.AGmath.AT

classification math.CTmath.AGmath.AT
keywords linearcategoriescategorycommutativedualizablefullyringadditional
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abstract

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 \'etale $R$-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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dualizable Additive Categories

    math.AT 2026-08 conditional novelty 8.0 of 10

    Dualizable additive categories are characterized intrinsically and via almost modules, and a universal finitary localizing invariant (prestable motives) is constructed whose unit corepresents algebraic K-theory.

  2. Is Crane--Yetter fully extended?

    math-ph 2025-06 conditional novelty 6.0 of 10

    Fully extended invertible 4D TQFTs valued in braided fusion categories form a Z/6-extension of the Witt group, so Crane-Yetter has six inequivalent point-refinements for fixed modular data.

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