The Stacks project

Lemma 85.21.2. Let $\mathcal{C}$ be a site with fibre product and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $a : U \to X$ be a hypercovering of $X$ in $\mathcal{C}$ as defined above. For $E \in D(\mathcal{C}/X)$ the map

\[ E \longrightarrow Ra_*a^{-1}E \]

is an isomorphism.

Proof. This is a special case of Lemma 85.19.2. $\square$

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