  We generalize the definition of satellites with respect to presheaves (and
copresheaves) with trace in the sense of Inassaridze; a presheaf with trace is
replaced by a graph with a pair of diagrams defined on it.
  We show that the right satellite functor is left adjoint to the left
satellite functor, and that a functor having a right (left) adjoint preserves
right (left) satellites.
  In particular cases the construction of satellites is given.
