The Stacks project

Lemma 72.7.5. 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 64.5.9. See also Spaces, Remark 64.5.2 in case you are confused about the meaning of this lemma. $\square$

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