International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 71, Pages 4501-4509
doi:10.1155/S0161171203209418

Atomical Grothendieck categories

C. Năstăsescu1 and B. Torrecillas2

 1Faculty of Mathematics, University of Bucharest, Bucharest 1 RO 70109, Romania
2Departmento de Álgebra y Análisis Matemático, Universidad de Almería, Almería 04071, Spain
Received 11 September 2002

Abstract

Motivated by the study of Gabriel dimension of a Grothendieck category, we introduce the concept of atomical Grothendieck category, which has only two localizing subcategories, and we give a classification of this type of Grothendieck categories.