Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for suc...Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for such category to be semiartinian. For semiartinian Grothendieck categories where every simple object has a projective cover, we obtain that every localizing subcategory is a TTF-class. In addition, some applications to semiperfect categories are obtained.展开更多
基金supported by Grant P07-FQM-03128 of Junta de Andaluciasupported by Grant 434/1.10.2007 0f CNCSIS,PN II(ID-1005)
文摘Using categorical techniques we obtain some results on localization and colocalization theory in Grothendieck categories with a set of small projective generators. In particular, we give a sufficient condition for such category to be semiartinian. For semiartinian Grothendieck categories where every simple object has a projective cover, we obtain that every localizing subcategory is a TTF-class. In addition, some applications to semiperfect categories are obtained.
