Definition 66.45.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

1. We say that $f$ is integral if for every affine scheme $Z$ and morphisms $Z \to Y$ the algebraic space $X \times _ Y Z$ is representable by an affine scheme integral over $Z$.

2. We say that $f$ is finite if for every affine scheme $Z$ and morphisms $Z \to Y$ the algebraic space $X \times _ Y Z$ is representable by an affine scheme finite over $Z$.

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