Lemma 76.14.2. 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 unramified,
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 unramified (as in More on Morphisms, Definition 37.6.1), and
for one such diagram with surjective vertical arrows the morphism \psi is formally unramified.
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