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monoidal category; monoidal functor; monoid; action; action of an object; semi-abelian category; semidirect product; groups; Lie algebras; crossed modules; actors
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.
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