Lemma 109.53.1. Let $S$ be a nonempty scheme. There exists a stack in groupoids $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ such that $p$ is limit preserving on objects, but $\mathcal{X}$ is not limit preserving.

Proof. See discussion above. $\square$

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