The Stacks project

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

  1. $U$ is an affine formal algebraic space,

  2. $\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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