  Frolicher and Nijenhuis recognized well in the middle of the previous century
that the Lie bracket and its Jacobi identity could and should exist beyond Lie
algebras. Nevertheless the conceptual meaning of their discovery has been
obscured by the messy techniques they exploited. The principal objective in
this paper is to show that the double dualization functor in a cartesian closed
category as well as synthetic differential geometry provides an adequate
framework, in which their discovery's conceptual meaning appears lucid.
