Lemma 66.4.10. Let $S$ be a scheme. Let $f : X \to Y$ and $g : Y \to Z$ be morphisms of algebraic spaces over $S$.

If $g \circ f$ is separated then so is $f$.

If $g \circ f$ is locally separated then so is $f$.

If $g \circ f$ is quasi-separated then so is $f$.

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