Abstract
The classical correspondance between groups and Lie algebras has been extended in the literature to various varieties of loops by associating a suitable type of algebras with each of them, e.g. Mal'cev algebras with Moufang loops and Sabinin algebras with all loops, mostly by using geometric methods. We will present a new, 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.
