Lie description of higher obstructions to deforming submanifolds

To every morphism chi : L -> M of differential graded Lie algebras we associate a functors of artin rings Def chi whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of chi. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kahler manifold is annihilated by the semiregularity map