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Flat covers and cotorsion envelopes of sheaves

Authors: Edgar Enochs and Luis Oyonarte
Journal: Proc. Amer. Math. Soc. 130 (2002), 1285-1292
MSC (2000): Primary 16G10, 18F20; Secondary 18E15
Published electronically: October 24, 2001
MathSciNet review: 1879949
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Abstract: In this paper we prove that any sheaf of modules over any topological space (in fact, any $\mathcal{O}$-module where $\mathcal{O}$ is a sheaf of rings on the topological space) has a flat cover and a cotorsion envelope. This result is very useful, as we shall explain later in the introduction, in order to compute cohomology, due to the fact that the category of sheaves ( $\mathcal{O}$-modules) does not have in general enough projectives.

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Additional Information

Edgar Enochs
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Luis Oyonarte
Affiliation: Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04071 Almería, Spain

Keywords: Flat (pre)cover, cotorsion (pre)envelope, (pre)sheaf, $\mathcal{O}$-(pre)module, Grothendieck category
Received by editor(s): July 26, 2000
Received by editor(s) in revised form: November 3, 2000
Published electronically: October 24, 2001
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society