Lemma 66.4.13. Let $S$ be a scheme. Let $f : X \to Y$ be a representable morphism of algebraic spaces over $S$.

The morphism $f$ is locally separated.

The morphism $f$ is (quasi-)separated in the sense of Definition 66.4.2 above if and only if $f$ is (quasi-)separated in the sense of Section 66.3.

In particular, if $f : X \to Y$ is a morphism of schemes over $S$, then $f$ is (quasi-)separated in the sense of Definition 66.4.2 if and only if $f$ is (quasi-)separated as a morphism of schemes.

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