Remark 7.25.11. Let $\mathcal{C}$ be a site. Let $U \to V$ be a morphism of $\mathcal{C}$. The cocontinuous functors $\mathcal{C}/U \to \mathcal{C}$ and $j : \mathcal{C}/U \to \mathcal{C}/V$ (Lemma 7.25.8) satisfy property $P$ of Remark 7.20.5. For example, if we have objects $(X/U)$, $(W/V)$, a morphism $g : j(X/U) \to (W/V)$, and a covering $\{ f_ i : (W_ i/V) \to (W/V)\}$ then $(X \times _ W W_ i/U)$ is an avatar of $(X/U) \times _{g, (W/V), f_ i} (W_ i/V)$ and the family $\{ (X \times _ W W_ i/U) \to (X/U)\}$ is a covering of $\mathcal{C}/U$.

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