## 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.

Lemma 73.18.1. The property $\mathcal{P}(f)=$“$f$ is smooth” is 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. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).