Lemma 10.155.6. Let $R \to S$ be a local map of local rings. Let $R \to R^ h$ and $S \to S^ h$ be the henselizations. There exists a unique local ring map $R^ h \to S^ h$ fitting into the commutative diagram

\[ \xymatrix{ R^ h \ar[r]_ f & S^ h \\ R \ar[u] \ar[r] & S \ar[u] } \]

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