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The Stacks project

Lemma 115.15.1. Let S be a scheme. Let X be an algebraic space over S. Let \{ f_ i : T_ i \to T\} _{i \in I} be a fpqc covering of schemes over S. Then the map

\mathop{\mathrm{Mor}}\nolimits _ S(T, X) \longrightarrow \prod \nolimits _{i \in I} \mathop{\mathrm{Mor}}\nolimits _ S(T_ i, X)

is injective.

Proof. Immediate consequence of Properties of Spaces, Proposition 66.17.1. \square

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