Internal object actions. (English) Zbl 1121.18004

Borceux, F.; Janelidze, G.; Kelly, G. M.

Commentat. Math. Univ. Carol. 46, No. 2, 235-255 (2005).

Summary: 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.

MSC:

18C15	Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
18C20	Eilenberg-Moore and Kleisli constructions for monads
18D10	Monoidal, symmetric monoidal and braided categories (MSC2010)
18D15	Closed categories (closed monoidal and Cartesian closed categories, etc.)

Keywords:

monoidal category; monoidal functor; monoid; action; semi-abelian category; semidirect product