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.
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