The Frolicher-Nijenhuis Calculus in Synthetic Differential Geometry
  Just as the Jacobi identity of vector fields is a natural consequence of the general Jacobi identity of microcubes in synthetic differential geometry, it is to be shown in this paper that the graded Jacobi identity of the Frolicher-Nijenhuis bracket is also a natural consequence of the general Jacobi identity. 
Hirokazu Nishimura