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...

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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
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cotorsion theory cogenerated by a set
cover
envelope
flat complex of modules
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description 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.
doi_str_mv 10.1006/jabr.2001.8821
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subjects cotorsion theory cogenerated by a set
cover
envelope
flat complex of modules
title Covers and Envelopes in Grothendieck Categories: Flat Covers of Complexes with Applications
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