Lemma 85.25.5. Let $U$ be a simplicial object of $\textit{LC}$ and let $a : U \to X$ be an augmentation. Let $\mathcal{A} \subset \textit{Ab}(U_{Zar})$ denote the weak Serre subcategory of cartesian abelian sheaves. If $U$ is a proper hypercovering of $X$, then the functor $a^{-1}$ defines an equivalence
\[ D^+(X) \longrightarrow D_\mathcal {A}^+(U_{Zar}) \]
with quasi-inverse $Ra_*$ where $a : \mathop{\mathit{Sh}}\nolimits (U_{Zar}) \to \mathop{\mathit{Sh}}\nolimits (X)$ is as in Lemma 85.2.8.
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