Abstract:We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.
Keywords: monoidal category, monoidal functor, monoid, action, action of an object, semi-abelian category, semidirect product, groups, Lie algebras, crossed modules, actors
AMS Subject Classification: 18C15, 18C20, 18D10, 18D15, 18G50