Lemma 91.27.1. In the situation above the category $\mathcal{C}_{X/\Lambda }$ is fibred over $X_{\acute{e}tale}$.

**Proof.**
Given an object $U \to \mathbf{A}$ of $\mathcal{C}_{X/\Lambda }$ and a morphism $U' \to U$ of $X_{\acute{e}tale}$ consider the object $U' \to \mathbf{A}$ of $\mathcal{C}_{X/\Lambda }$ where $U' \to \mathbf{A}$ is the composition of $U \to \mathbf{A}$ and $U' \to U$. The morphism $(U' \to \mathbf{A}) \to (U \to \mathbf{A})$ of $\mathcal{C}_{X/\Lambda }$ is strongly cartesian over $X_{\acute{e}tale}$.
$\square$

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