Lemma 29.3.1. Let $Z \to Y \to X$ be morphisms of schemes.

If $Z \to X$ is an immersion, then $Z \to Y$ is an immersion.

If $Z \to X$ is a quasi-compact immersion and $Y \to X$ is quasi-separated, then $Z \to Y$ is a quasi-compact immersion.

If $Z \to X$ is a closed immersion and $Y \to X$ is separated, then $Z \to Y$ is a closed immersion.

## Comments (6)

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