  A seminal result of Agler characterizes the so-called Schur-Agler class of
functions on the polydisk in terms of a unitary colligation transfer function
representation. We generalize this to the unit ball of the algebra of
multipliers for a family of test functions over a broad class of semigroupoids.
There is then an associated interpolation theorem. Besides leading to solutions
of the familiar Nevanlinna-Pick and Caratheodory-Fejer interpolation problems
and their multivariable commutative and noncommutative generalizations, this
approach also covers more exotic examples.
