Lemma 99.15.4 (0D53)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 99: Quot and Hilbert Spaces
Section 99.15: The stack of curves
Lemma 99.15.4 (cite)

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\[ \Delta : \mathcal{C}\! \mathit{urves}\longrightarrow \mathcal{C}\! \mathit{urves}\times \mathcal{C}\! \mathit{urves} \]

is representable by algebraic spaces.

Proof. This is immediate from the fully faithful embedding (99.15.1.1) and the corresponding fact for $\mathcal{S}\! \mathit{paces}'_{fp, flat, proper}$ (Lemma 99.13.2). $\square$

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