Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications

In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of F-covers and envelopes to the study of some properties of the class F. We then prove the existence of flat covers and cotorsion env...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2001-09, Vol.243 (2), p.615-630
Main Authors: Aldrich, S.Tempest, Enochs, Edgar E, Garcı́a Rozas, J.R, Oyonarte, Luis
Format: Article
Language:English
Subjects:
cotorsion theory cogenerated by a set
cover
envelope
flat complex of modules
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the general setting of Grothendieck categories with enough projectives, we prove theorems that make possible to restrict the study of the problem of the existence of F-covers and envelopes to the study of some properties of the class F. We then prove the existence of flat covers and cotorsion envelopes of complexes, giving some examples. This generalizes the earlier work (J. Algebra201 (1998), 86–102) and finishes the problem of the existence of flat covers of complexes.
ISSN:0021-8693
1090-266X
DOI:10.1006/jabr.2001.8821