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Internal object actions

Francis Borceux, George Z. Janelidze, Gregory Maxwell Kelly (2005)

Commentationes Mathematicae Universitatis Carolinae

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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