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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