Djament's Problem on Locally Noetherian Grothendieck Categories
Statement
Djament asked whether a Grothendieck category satisfying suitable finiteness and exactness conditions must be equivalent to a module category. In the locally noetherian case the answer is no: there is a Grothendieck category with a noetherian generator satisfying AB4* that is not equivalent to a module category, built as a Gabriel quotient of a module category over an endomorphism ring of Herbera, Prihoda and Wiegand.
Record
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
Ryo Kanda, using ChatGPT (GPT-5.5, GPT-5.6)That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The disclosure attributes two specific things. The tool suggested examining the example in Section 8 of Herbera-Prihoda-Wiegand as a possible source of a negative answer, which is the example the paper is built on, and it suggested a proof strategy. The author independently checked that strategy and supplied the proof.
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