Lemma 84.15.1. Let $\mathcal{C}$ be a site.

For $K$ in $\text{SR}(\mathcal{C})$ the functor $j : \mathcal{C}/K \to \mathcal{C}$ is continuous, cocontinuous, and has property P of Sites, Remark 7.20.5.

For $f : K \to L$ in $\text{SR}(\mathcal{C})$ the functor $v : \mathcal{C}/K \to \mathcal{C}/L$ (see above) is continuous, cocontinuous, and has property P of Sites, Remark 7.20.5.

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