Lemma 73.7.5 (0469)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 73: Topologies on Algebraic Spaces
Section 73.7: Fppf topology
Lemma 73.7.5 (cite)

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Lemma 73.7.5. Let $S$ be a scheme. Let $\{ f_ i : X_ i \to X\} _{i \in I}$ be an fppf covering of algebraic spaces over $S$ . Then the map of sheaves

$\coprod X_ i \longrightarrow X$

is surjective.

Proof. This follows from Spaces, Lemma 65.5.9. See also Spaces, Remark 65.5.2 in case you are confused about the meaning of this lemma. $\square$

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