Algebraic functor calculus and commutator theory
Résumé
Classically, Lie algebras can be considered as linearizations of groups in several ways, and thus provide key tools in group theory. With the emergence of more and more other non-linear algebraic structures the problem arises to generalize the relations between groups and Lie algebras to a much broader context. A categorical approach to this problem will be
presented starting out from a new notion of commutator and lower central series deduced from the cross-effects of the identity functor. Lie algebras then generalize to algebras over linear or, more generally, multilinear functor operads.