Formally smooth map
In algebraic geometry and commutative algebra, a ring homomorphism f : A → B {\displaystyle f:A\to B} is called formally smooth (from French: Formellement lisse) if it satisfies the following infinitesimal lifting property: Suppose B is given the structure of an A-algebra via the map f. Given a commutative A-algebra, C, and a nilpotent ideal N ⊆ C {\displaystyle N\subseteq C} , any A-algebra homomorphism B → C / N {\displaystyle B\to C/N} may be lifted to an A-algebra map B → C {\displaystyle B\to C} .