The Stacks project

Lemma 83.4.2. Let $S$ be a scheme, and let $B$ be an algebraic space over $S$. Let $j : R \to U \times _ B U$ be a pre-relation in algebraic spaces over $B$. If a categorical quotient in the category of algebraic spaces over $B$ exists, then it is unique up to unique isomorphism. Similarly for categorical quotients in full subcategories of $\textit{Spaces}/B$.

Proof. See Categories, Section 4.11. $\square$

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