Lemma 63.45.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The following are equivalent

$f$ is integral, and

$f$ is affine and universally closed.

Lemma 63.45.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. The following are equivalent

$f$ is integral, and

$f$ is affine and universally closed.

**Proof.**
In both cases the morphism is representable, and you can check the condition after a base change by an affine scheme mapping into $Y$, see Lemmas 63.45.3, 63.20.3, and 63.9.5. Hence the result follows from Morphisms, Lemma 28.42.7.
$\square$

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