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The Stacks project

Lemma 85.21.3. Let \mathcal{C} be a site with fibre products 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. Then we have a canonical isomorphism

R\Gamma (X, E) = R\Gamma ((\mathcal{C}/U)_{total}, a^{-1}E)

for E \in D(\mathcal{C}/X).

Proof. This is a special case of Lemma 85.19.3. \square

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