A representation of locally Artinian categories (Q1057356)

A Grothendieck category \({\mathcal C}\) is said to be locally Artinian if it has a set of generators which are Artinian objects. The author shows that a Grothendieck category \({\mathcal C}\) is locally Artinian if and only if it is naturally equivalent with the category of all discrete right R-modules over a right topologically Artinian ring R.