Lemma 21.24.1. In the situation described above. Denote $\mathcal{H}^ m = H^ m(\mathcal{F}^\bullet )$ the $m$th 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 $q < 0$

^{1}.

Then (21.24.0.1) is a quasi-isomorphism.

## Comments (0)