Lemma 25.4.5. Let $\mathcal{C}$ be a site with fibre products. Let $X$ be an object of $\mathcal{C}$. Let $K$ be a hypercovering of $X$. The homology of the simplicial presheaf $F(K)$ is $0$ in degrees $> 0$ and equal to $\mathbf{Z}_ X^\#$ in degree $0$.

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