Lemma 78.8.1. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $B$. Let $g : U' \to U$ be a morphism of algebraic spaces over $B$. Let $(U', R', s', t', c')$ be the restriction of $(U, R, s, t, c)$ via $g$.

If $s, t$ are locally of finite type and $g$ is locally of finite type, then $s', t'$ are locally of finite type.

If $s, t$ are locally of finite presentation and $g$ is locally of finite presentation, then $s', t'$ are locally of finite presentation.

If $s, t$ are flat and $g$ is flat, then $s', t'$ are flat.

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