= Resolution principle for sheaf cohomology
If $0\to\mathcal F\to\mathcal A^0\to\mathcal A^1\to\cdots$ is an <exact sequence> of <sheaves of abelian groups> on $X$ and $H^q(X,\mathcal A^j)=0$ for every $q>0$ and $j\geq0$, then <sheaf cohomology> is computed by the <cochain complex> of global sections:
$$
H^i(X,\mathcal F)\cong H^i\bigl(\Gamma(X,\mathcal A^\bullet)\bigr).
$$
In particular a <flasque resolution> computes sheaf cohomology. Acyclicity is required on the space on which cohomology is being computed.
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