Definition 15.36.1. Let $R \to S$ be a homomorphism of topological rings with $R$ and $S$ linearly topologized. We say $S$ is formally smooth over $R$ if for every commutative solid diagram

$\xymatrix{ S \ar[r] \ar@{-->}[rd] & A/J \\ R \ar[r] \ar[u] & A \ar[u] }$

of homomorphisms of topological rings where $A$ is a discrete ring and $J \subset A$ is an ideal of square zero, a dotted arrow exists which makes the diagram commute.

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