Locally finitely presented Grothendieck categories and the pure semisimplicity conjecture
Locally finitely presented Grothendieck categories and the pure semisimplicity conjecture
Abstract In this paper, we investigate locally finitely presented pure semisimple (hereditary) Grothendieck categories. We show that every locally finitely presented pure semisimple (resp., hereditary) Grothendieck category $\mathscr {A}$ is equivalent to the category of left modules over a left pure semisimple (resp., left hereditary) ring when $\mathrm {Mod}(\mathrm {fp}(\mathscr …