The Gabriel–Popescu theorem states that any Grothendieck category \mathcal{A} is equivalent to a Serre quotient of the form \operatorname{Mod}(R)/\cal{B}, where \operatorname{Mod}(R) denotes the abelian category of right modules over some unital ring R, and \cal{B} is some localizing subcategory of \operatorname{Mod}(R).
