Lemma 75.13.5. Let $S$ be a scheme. Let $F, G : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Let $a : F \to G$ be a representable transformation of functors.

If $a$ is smooth then $a$ is formally smooth.

If $a$ is étale, then $a$ is formally étale.

If $a$ is unramified, then $a$ is formally unramified.

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