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arXiv · 2405.16468

Module-theoretic approach to dualizable Grothendieck categories

Ryo Kanda
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Abstract

We prove that every dualizable Grothendieck category whose dual is again a Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by taking a module-theoretic approach based on the Gabriel-Popescu embedding. Combining this with a result by Stefanich, we conclude that the class of dualizable linear cocomplete categories is precisely the class of linear Grothendieck category satisfying Ab6 and Ab4*. This provides a complete answer to a modified conjecture on the dualizability, originally posed by Brandenburg, Chirvasitu, and Johnson-Freyd.

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Ryo Kanda. 2024-05-26. Module-theoretic approach to dualizable Grothendieck categories. https://arxiv.org/abs/2405.16468

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