On monads of exact reflective localizations of Abelian categories

Abstract

In this paper we define Gabriel monads as the idempotent monads associated to exact reflective localizations 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.

fixed Prop. 2.10, updated bibliography

References in corpus (2)

• Characterizing Serre quotients with no section functor and applications to coherent sheaves
• On the Ext-computability of Serre quotient categories

Cited by in corpus (5)

• Gauge Backgrounds and Zero-Mode Counting in F-Theory
• On the Ext-computability of Serre quotient categories
• Characterizing Serre quotients with no section functor and applications to coherent sheaves
• Gabriel morphisms and the computability of Serre quotients with applications to coherent sheaves
• A constructive approach to the module of twisted global sections on relative projective spaces