Lemma 24.7.2. Let $\mathcal{C}$ be a site with fibre products. Let $X$ be an object of $\mathcal{C}$. If $K, L$ are hypercoverings of $X$, then $K \times L$ is a hypercovering of $X$.

Proof. You can either verify this directly, or use Lemma 24.7.1 above and check that $L \to \{ X \to X\}$ has property (3). $\square$

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