Lemma 85.20.1. Let $\mathcal{C}$ be a site with fibre products and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $\mathcal{O}_\mathcal {C}$ be a sheaf of rings. Let $K$ be a hypercovering of $X$. With notation as above

is fully faithful with essential image the cartesian $\mathcal{O}$-modules. The functor $a_*$ provides the quasi-inverse.

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