Lemma 15.44.2. Let $(R, \mathfrak m, \kappa )$ be a local ring. Then

$R \to R^ h$, $R^ h \to R^{sh}$, and $R \to R^{sh}$ are formally étale,

$R \to R^ h$, $R^ h \to R^{sh}$, resp. $R \to R^{sh}$ are formally smooth in the $\mathfrak m^ h$, $\mathfrak m^{sh}$, resp. $\mathfrak m^{sh}$-topology.

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