Lemma 73.18.1. The property $\mathcal{P}(f)=$“$f$ is smooth” is smooth local on the source.

## 73.18 Properties of morphisms local in the smooth topology on the source

Here are some properties of morphisms that are smooth local on the source.

**Proof.**
Follows from Lemma 73.14.3 using Morphisms of Spaces, Definition 66.37.1 and Descent, Lemma 35.30.1.
$\square$

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