We will present the foundations of a new, algebraic (actually functor theoretic) approach allowing to construct analogous linearizations in a much broader context, consisting of a suitable linear operad associated with any semi-abelian category. This operad recovers the types of algebras previously associated with groups and numerous varieties of loops. Extending the classical Lazard correspondance and Baker-Campbell- Hausdorff formula to this framework using polynomial functor theory instead of the exponential function is an ongoing project.In this second talk we continue the discussion of commutators with the aid of the concept of polynomial functors, and sketch the construction of the operad associated with a semi-abelian category or, more specifically, semi-abelian variety of universal algebras. Finally a Lazard type correspondance and Baker-Campbell-Hausdorff formula for 2-divisible 2-nilpotent varieties will be presented.