Lemma 92.27.1 (08VJ)—The Stacks project

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Table of contents
Part 6: Deformation Theory
Chapter 92: The Cotangent Complex
Section 92.27: The cotangent complex of an algebraic space over a ring
Lemma 92.27.1 (cite)

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Lemma 92.27.1. 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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