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I have a doubt, I read somewhere that the Godement resolution of a sheaf $\mathcal{F}$ is a quasi-isomorphism

$\mathcal{F} \rightarrow C^\bullet(\mathcal{F})$.

Just right off the bat when I read that I was like, aren't quasi-isomorphisms supposed to be between complexes? How do I interpret that? Should I interpret it as a quasi-isomorphism

$\mathcal{F}^\bullet \rightarrow C^p(\mathcal{F}^\bullet)$

for all $p$?

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    If I understand [this](http://en.wikipedia.org/wiki/Godement_resolution) correctly, then the Godement construction is a way to produce a flabby resolution $C^{\bullet}(\mathcal{F})$ of a given sheaf $\mathcal{F}$. If you interpret $\mathcal{F}$ as a complex concentrated in degree zero, then there is a quasi-isomorphism $\mathcal{F} \to C^{\bullet}(\mathcal{F})$.2012-08-24
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    Yeah, it kind of makes sense now, thanks so much for your help2012-08-24

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