The Stacks project

Remark 68.6.3. Reasonable algebraic spaces are technically easier to work with than very reasonable algebraic spaces. For example, if $X \to Y$ is a quasi-compact étale surjective morphism of algebraic spaces and $X$ is reasonable, then so is $Y$, see Lemma 68.17.8 but we don't know if this is true for the property “very reasonable”. Below we give another technical property enjoyed by reasonable algebraic spaces.

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