Lemma 84.17.5. Let $\mathcal{C}$ be a site with equalizers and fibre products. Let $K$ be a hypercovering. Let $\mathcal{A} \subset \textit{Ab}((\mathcal{C}/K)_{total})$ denote the weak Serre subcategory of cartesian abelian sheaves. Then the functor $a^{-1}$ defines an equivalence

with quasi-inverse $Ra_*$.

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