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 (4)

Comment #733 by Kestutis Cesnavicius on

Comment #739 by Johan on

Comment #4342 by Kazuki Masugi(馬杉和貴) on

Comment #4492 by Johan on