Localization on certain Grothendieck categories |
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| Authors: | F Castaño-Iglesias N Chifan C Năstăsescu |
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| Institution: | (1) Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Almería, Spain;(2) Department of Mathematics, University of Galati, Galati, Romania;(3) Facultatea de Matematică, Str. Academiei 14, RO-70109 Bucharest, Romania |
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| Abstract: | 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.
Research supported by Grant 434/1.10.2007 of CNCSIS, PN II (ID 1005) |
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| Keywords: | Grothendieck category localization colocalization semiartinian category semiperfect category |
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