Geodesic
Internal object actions
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 2, pp. 235-255.

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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.
Classification : 18C15, 18C20, 18D10, 18D15, 18G50
Keywords: monoidal category; monoidal functor; monoid; action; action of an object; semi-abelian category; semidirect product; groups; Lie algebras; crossed modules; actors 
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     title = {Internal object actions},
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Borceux, F.; Janelidze, G.; Kelly, G. M. Internal object actions. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 2, pp. 235-255. http://geodesic.mathdoc.fr/item/CMUC_2005__46_2_a2/