Lemma 21.24.1. In the situation described above. Denote \mathcal{H}^ m = H^ m(\mathcal{F}^\bullet ) the mth cohomology sheaf. Let \mathcal{B} \subset \mathop{\mathrm{Ob}}\nolimits (\mathcal{C}) be a subset. Let d \in \mathbf{N}. Assume
every object of \mathcal{C} has a covering whose members are elements of \mathcal{B},
for every U \in \mathcal{B} we have H^ p(U, \mathcal{H}^ q) = 0 for p > d and q < 01.
Then (21.24.0.1) is a quasi-isomorphism.
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