A Grothendieck category with a noetherian generator and exact products that is not a module category

Ryo Kanda

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arXiv · 2607.23520

A Grothendieck category with a noetherian generator and exact products that is not a module category

Ryo Kanda

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Abstract

We construct a Grothendieck category that has a noetherian generator, satisfies AB4*, and is not equivalent to a module category. This gives a negative answer to Djament's problem. The category is obtained as a Gabriel quotient of a module category over the endomorphism ring appearing in the work of Herbera, P\v{r}\'{\i}hoda, and Wiegand. The proof relies on the trace criterion established by Martini, Parra, Saor\'{\i}n, and Virili.

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Ryo Kanda. 2026-07-26. A Grothendieck category with a noetherian generator and exact products that is not a module category. https://arxiv.org/abs/2607.23520

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