Lemma 39.20.3. In the situation of Definition 39.20.1. Assume there is a scheme $M$, and a morphism $U \to M$ such that

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

the morphism $U \to M$ induces a surjection of sheaves $h_ U \to h_ M$ in the $\tau $-topology, and

the induced map $(t, s) : R \to U \times _ M U$ induces a surjection of sheaves $h_ R \to h_{U \times _ M U}$ in the $\tau $-topology.

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

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