Lemma 7.47.5. Let $\mathcal{C}$ be a category. Let $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $S$ be a sieve on $U$. If $f : V \to U$ is in $S$, then $S \times _ U V = h_ V$ is maximal.

**Proof.**
Trivial from the definitions.
$\square$

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