Definition 37.11.1. Let $f : X \to S$ be a morphism of schemes. We say $f$ is *formally smooth* if given any solid commutative diagram

\[ \xymatrix{ X \ar[d]_ f & T \ar[d]^ i \ar[l] \\ S & T' \ar[l] \ar@{-->}[lu] } \]

where $T \subset T'$ is a first order thickening of affine schemes over $S$ there exists a dotted arrow making the diagram commute.

## Comments (0)

There are also: