Gabriel localization in functor categories

Abstract

P. Gabriel showed that for a unital ring R, there exists a bijective correspondece between the set of Gabriel filters of R and the set of Giraud subcategories of Mod(R) (see [Gab62, Lemme 1] on page 412). In this paper we prove an analogous of Gabriel's result: for an small preadditive category C, there exists a bijective correspondence between the Gabriel filters of C and Giraud subcategories of Mod(C).