Lemma 85.19.3. Let $\mathcal{C}$ be a site with fibre products and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $K$ be a hypercovering of $X$. Then we have a canonical isomorphism

for $E \in D(\mathcal{C}/X)$.

Lemma 85.19.3. Let $\mathcal{C}$ be a site with fibre products and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $K$ be a hypercovering of $X$. Then we have a canonical isomorphism

\[ R\Gamma (X, E) = R\Gamma ((\mathcal{C}/K)_{total}, a^{-1}E) \]

for $E \in D(\mathcal{C}/X)$.

**Proof.**
Via Remarks 85.15.5 and 85.16.4 this follows from Lemma 85.17.4.
$\square$

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