The Stacks project

Lemma 78.11.2. Let $B \to S$ as in Section 78.3. Given a groupoid in algebraic spaces $(U, R, s, t, c)$ over $B$ the morphism $j : R \to U \times _ B U$ is a pre-equivalence relation.

Proof. Omitted. This is a nice exercise in the definitions. $\square$

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