Lemma 96.14.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Then $\mathcal{H}_ d(X)$ is an algebraic stack.

Proof. The $1$-morphism

$\mathcal{H}_ d(X) \longrightarrow \mathcal{H}_ d$

is representable by algebraic spaces according to Lemma 96.12.6. The stack $\mathcal{H}_ d$ is an algebraic stack according to Proposition 96.13.2. Hence $\mathcal{H}_ d(X)$ is an algebraic stack by Algebraic Stacks, Lemma 93.15.4. $\square$

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