Lemma 87.34.7 (0DEH)—The Stacks project

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Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.34: The small étale site of a formal algebraic space
Lemma 87.34.7 (cite)

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Lemma 87.34.7. Let $S$ be a scheme. Let $X$ be a formal algebraic space over $S$ . Then $X_{affine, {\acute{e}tale}}$ is equivalent to the category whose objects are morphisms $\varphi : U \to X$ of formal algebraic spaces such that

$U$ is an affine formal algebraic space,
$\varphi$ is representable by algebraic spaces and étale.

Proof. This follows by combining Lemmas 87.34.6 and 87.18.3. $\square$

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