  Given a fibration in groupoids d : D -> I, we define a fibered multicategory
as a particular functor p : M -> I, where M has the same objects as D, and its
arrows a : X -> Y should be thought of as families of arrows in the
multicategory, indexed by pY. The key axiom extends the reindexing of objects,
given by d, to a reindexing of arrows in M along pullback squares in I. When D
is included in M, in an appropriate sense, one gets again fibered categories.
  In this context, cartesian fibered multicategories are defined and studied in
a natural way.
