The complexification of Lie algebras determines a functor from real Lie algebras to complex Lie algebras, whose right adjoint is the restriction of scalars functor. Thus, we know that complexification of Lie algebras is right exact and cocontinuous.
Are there are any other essential properties that this functor has? I assume it is faithful, but is it full? Does it reflect any properties? Is it also left exact?
I am wondering about properties that it has as a functor between categories of Lie algebras, not just of vector spaces.