An L∞-algebra of an unobstructed deformation functor

This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on the simple observation that the Kuranishi map can always be inverted in the category of L∞-algebras. The L∞-structure obtained by this inversion is used to define an unobstructed deformation functor, which is always representable by a smooth pointed moduli space. The singular nature of the originial Kuranishi deformation space emerges in this setting merely as a result of the truncation of the naive L∞-algebra controlling the deformations to a usual differential Lie algebra.