nLab
Gabriel-Oberst duality

The category Ab of discrete abelian groups is (as a case of Pontrjagin duality for locally compact Hausdorff groups) dual category to the category of compact Hausdorff abelian groups.

Gabriel-Roos-Oberst duality refers to several generalizations of this duality for more general Grothendieck categories in terms of linearly compact topological rings and modules.

In Gabriel’s thesis

the dual of any locally finite Grothendieck category has been found. Roos has generalized this to locally noetherian Grothendieck categories in

The case of (dual of) a general Grothendieck category is found in

A textbook exposition is in the chapter 6, Duality of