The Stacks project

Lemma 97.5.4. Let $p : \mathcal{X} \to \mathcal{Y}$ be a $1$-morphism of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Assume $p$ is representable by algebraic spaces and an open immersion. Then $p$ is limit preserving on objects.

Proof. This follows from Lemma 97.5.3 and (via the general principle Algebraic Stacks, Lemma 94.10.9) from the fact that an open immersion of algebraic spaces is locally of finite presentation, see Morphisms of Spaces, Lemma 67.28.11. $\square$

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