Definition 66.16.2 (03FR)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.16: Étale morphisms of algebraic spaces
Definition 66.16.2 (cite)

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Definition 66.16.2. Let $S$ be a scheme. A morphism $f : X \to Y$ between algebraic spaces over $S$ is called étale if and only if for every étale morphism $\varphi : U \to X$ where $U$ is a scheme, the composition $f \circ \varphi $ is étale also.

Comments (2)

Comment #2317 by Nithi Rungtanapirom on December 07, 2016 at 16:45

In the last clause, the composition $\varphi\circ f$ should read $f\circ\varphi$ .

Comment #2393 by Johan on February 17, 2017 at 01:08

Thanks. Fixed here.

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