Definition 35.33.1 (04NB)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.33: Properties of morphisms of germs local on source-and-target
Definition 35.33.1 (cite)

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Definition 35.33.1. Let $\mathcal{Q}$ be a property of morphisms of germs of schemes. We say $\mathcal{Q}$ is étale local on the source-and-target if for any commutative diagram

$\xymatrix{ (U', u') \ar[d]_ a \ar[r]_{h'} & (V', v') \ar[d]^ b \\ (U, u) \ar[r]^ h & (V, v) }$

of germs with étale vertical arrows we have $\mathcal{Q}(h) \Leftrightarrow \mathcal{Q}(h')$ .

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