Inner actions and Galois -objects in a symmetric closed category
Internal object actions
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.
Internal presheaves toposes
Isomorphisms between left and right adjoints.