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 $p$?