Lemma 76.16.2. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. The following are equivalent:
f is formally étale,
for every diagram
\xymatrix{ U \ar[d] \ar[r]_\psi & V \ar[d] \\ X \ar[r]^ f & Y }where U and V are schemes and the vertical arrows are étale the morphism of schemes \psi is formally étale (as in More on Morphisms, Definition 37.8.1), and
for one such diagram with surjective vertical arrows the morphism \psi is formally étale.
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