Lemma 18.28.2 (03ES)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 18: Modules on Sites
Section 18.28: Flat modules
Lemma 18.28.2 (cite)

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Lemma 18.28.2. Let $\mathcal{C}$ be a category. Let $\mathcal{O}$ be a presheaf of rings. Let $\mathcal{F}$ be a presheaf of $\mathcal{O}$ -modules. If each $\mathcal{F}(U)$ is a flat $\mathcal{O}(U)$ -module, then $\mathcal{F}$ is flat.

Proof. This is immediate from the definitions. $\square$

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