Lemma 66.45.1. Let $S$ be a scheme. Let $f : X \to Y$ be a representable morphism of algebraic spaces over $S$. Then $f$ is integral, resp. finite (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 affine and integral, resp. finite, over $Z$.
Proof. This follows directly from the definition of an integral (resp. finite) morphism of schemes (Morphisms, Definition 29.44.1). $\square$
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