  Given a diagram of Pi-algebras (graded groups equipped with an action of the
primary homotopy operations), we ask whether it can be realized as the homotopy
groups of a diagram of spaces. The answer given here is in the form of an
obstruction theory, of somewhat wider application, formulated in terms of
generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg.
103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization
of a single Pi-algebra. In particular, we explicitly analyze the simple case of
a single map, and provide a detailed example, illustrating the connections to
higher homotopy operations.
