Lemma 85.19.2. Let $\mathcal{C}$ be a site with fibre product and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $K$ be a hypercovering of $X$. For $E \in D(\mathcal{C}/X)$ the map

is an isomorphism.

Lemma 85.19.2. Let $\mathcal{C}$ be a site with fibre product and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $K$ be a hypercovering of $X$. For $E \in D(\mathcal{C}/X)$ the map

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

is an isomorphism.

**Proof.**
Via Remarks 85.15.5 and 85.16.4 and the discussion in the introduction to this section this follows from Lemma 85.17.3.
$\square$

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