Lemma 75.16.6. 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,

$f$ is formally unramified and the universal first order thickening of $X$ over $Y$ is equal to $X$,

$f$ is formally unramified and $\mathcal{C}_{X/Y} = 0$, and

$\Omega _{X/Y} = 0$ and $\mathcal{C}_{X/Y} = 0$.

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