Lemma 77.11.3. Let $B \to S$ as in Section 77.3. Given an equivalence relation $j : R \to U \times _ B U$ over $B$ there is a unique way to extend it to a groupoid in algebraic spaces $(U, R, s, t, c)$ over $B$.

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

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