Lemma 75.16.2. 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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