Flat covers and cotorsion envelopes of sheaves

Enochs, Edgar; Oyonarte, Luis

doi:10.1090/S0002-9939-01-06190-1

Flat covers and cotorsion envelopes of sheaves
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by Edgar Enochs and Luis Oyonarte PDF

Proc. Amer. Math. Soc. 130 (2002), 1285-1292 Request permission

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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