Localization in categories of complexes and unbounded resolutions

Authors
Tarrio, LA Lopez, AJ Salorio, MJS
Citation
La. Tarrio et al., Localization in categories of complexes and unbounded resolutions, CAN J MATH, 52(2), 2000, pp. 225-247
Citations number
24
Categorie Soggetti
Mathematics
Journal title
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN journal
0008414X → ACNP
Volume
52
Issue
2
Year of publication
2000
Pages
225 - 247
Database
ISI
SICI code
0008-414X(200004)52:2<225:LICOCA>2.0.ZU;2-W
Abstract
In this paper we show that for a Grothendieck category A and a complex E in C(A) there is an associated localization endofunctor l in D(A). This means that l is idempotent tin a natural way) and that the objects that go to 0 by l are those of the smallest localizing (= triangulated and stable for co products) subcategory of D(A) that contains E. As applications, we construc t K-injective resolutions for complexes of objects of A and derive Brown re presentability for D(A) from the known result for D(R-mod), where R is a ri ng with unit.