Lemma 77.19.4. In the situation of Definition 77.19.1. Assume there is an algebraic space $M$ over $S$, and a morphism $U \to M$ such that

the morphism $U \to M$ equalizes $s, t$,

the map $U \to M$ is a surjection of sheaves, and

the induced map $(t, s) : R \to U \times _ M U$ is a surjection of sheaves.

In this case $M$ represents the quotient sheaf $U/R$.

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