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The Stacks project

Lemma 108.10.1. The diagonal of $\mathit{Mor}_ B(Y, X) \to B$ is a closed immersion of finite presentation.

Proof. There is an open immersion $\mathit{Mor}_ B(Y, X) \to \mathrm{Hilb}_{Y \times _ B X/B}$, see Quot, Lemma 99.12.2. Thus the lemma follows from Lemma 108.7.1. $\square$

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