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Jun 18, 2020 at 11:13 comment added Leonid Positselski @AurélienDjament Yes, you are right. Thank you.
Jun 18, 2020 at 6:24 comment added Aurélien Djament "On the other hand, I am not aware of any example of a category with a generator, with infinite direct sums, in which all short exact sequences split, but which is not Grothendieck.": taking the opposite category of any non-zero spectral Grothendieck category gives an example.
Jun 17, 2020 at 18:12 vote accept Jake Wetlock
Jun 17, 2020 at 16:10 history answered Leonid Positselski CC BY-SA 4.0