Definition 29.23.1. Let $f : X \to Y$ be a morphism of schemes.

## 29.23 Submersive morphisms

We note that a submersive morphism is in particular surjective.

Lemma 29.23.2. The base change of a universally submersive morphism of schemes by any morphism of schemes is universally submersive.

**Proof.**
This is immediate from the definition.
$\square$

Lemma 29.23.3. The composition of a pair of (universally) submersive morphisms of schemes is (universally) submersive.

**Proof.**
Omitted.
$\square$

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## Comments (2)

Comment #4577 by Andy on

Comment #4578 by Andy on