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.
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.