Godement resolution
= Godement resolution
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Embed a <sheaf of abelian groups> $\mathcal F$ into the sheaf $C(\mathcal F)(U)=\prod_{P\in U}\mathcal F_P$ by all its <germs>. Restrictions are projections, so $C(\mathcal F)$ is <flasque>. Repeat on the successive sheaf <cokernels> to obtain a canonical <flasque resolution>. Its complex of <global sections> computes <sheaf cohomology>. When $\mathcal F$ is itself <flasque>, the flasque-kernel section-lifting lemma makes every successive quotient flasque and makes the global-section complex exact in positive degrees, proving $H^q(X,\mathcal F)=0$ for $q>0$ without assuming that vanishing in the construction.