Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

On monads of exact reflective localizations of Abelian categories

Pages: 145 – 151

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a8

Authors

Mohamed Barakat (Department of Mathematics, University of Kaiserslautern, Germany)

Markus Lange-Hegermann (Lehrstuhl B für Mathematik, RWTH Aachen University, Aachen, Germany)

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.

Keywords

Serre quotient, reflective localization of Abelian categories, idempotent monad, Gabriel localization, saturating monad

2010 Mathematics Subject Classification

18A40, 18E35

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