Lemma 65.9.1. Let F be an algebraic space over S. Let f : U \to F be a surjective étale morphism from a scheme to F. Set R = U \times _ F U. Then
j : R \to U \times _ S U defines an equivalence relation on U over S (see Groupoids, Definition 39.3.1).
the morphisms s, t : R \to U are étale, and
the diagram
\xymatrix{ R \ar@<1ex>[r] \ar@<-1ex>[r] & U \ar[r] & F }is a coequalizer diagram in \mathop{\mathit{Sh}}\nolimits ((\mathit{Sch}/S)_{fppf}).
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