Lemma 99.15.4. The diagonal

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

is representable by algebraic spaces.

Lemma 99.15.4. The diagonal

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

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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