The Stacks project

Lemma 76.3.2. A radicial morphism of algebraic spaces is universally injective.

Proof. Let $S$ be a scheme. Let $f : X \to Y$ be a radicial morphism of algebraic spaces over $S$. It is clear from the definition that given a morphism $\mathop{\mathrm{Spec}}(K) \to Y$ there is at most one lift of this morphism to a morphism into $X$. Hence we conclude that $f$ is universally injective by Morphisms of Spaces, Lemma 67.19.2. $\square$

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