On monads of exact reflective localizations of abelian categories (Q384299)

Abelian categories became a central notion in homological algebra. In this paper the authors define Gabriel monads as the idempotent monads associated to exact reflective localization in abelian categories and characterize them by a simple set of properties. The coimage of a Gabriel monad is a Serre quotient category. The Gabriel monad induces an equivalence between its coimage and its image, the localizing subcategory of local objects.