Lemma 74.18.1 (06F2)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 74: Descent and Algebraic Spaces
Section 74.18: Properties of morphisms local in the smooth topology on the source
Lemma 74.18.1 (cite)

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Lemma 74.18.1. The property $\mathcal{P}(f)=$ “ $f$ is smooth” is smooth local on the source.

Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.37.1 and Descent, Lemma 35.30.1. $\square$

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