Lemma 75.16.3. Let $S$ be a scheme. Let $f : X \to Y$ be a formally étale morphism of algebraic spaces over $S$. Then given any solid commutative diagram

where $T \subset T'$ is a first order thickening of algebraic spaces over $Y$ there exists exactly one dotted arrow making the diagram commute. In other words, in Definition 75.16.1 the condition that $T$ be affine may be dropped.

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