The Stacks project

Lemma 66.21.1. Let $S$ be a scheme. Let $f : X \to Y$ be a representable morphism of algebraic spaces over $S$. Then $f$ is quasi-affine (in the sense of Section 66.3) if and only if for all affine schemes $Z$ and morphisms $Z \to Y$ the scheme $X \times _ Y Z$ is quasi-affine.

Proof. This follows directly from the definition of a quasi-affine morphism of schemes (Morphisms, Definition 29.13.1). $\square$

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