Djament's Problem on Locally Noetherian Grothendieck Categories
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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.
Context
the locally noetherian case; whether such a category can fail to admit a projective generator is left open as Problem 1.3
A named problem about when Grothendieck categories are module categories, restated as Problem 5.13 by Martini, Parra, Saorin and Virili.
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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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