  In this paper, we extend Ocneanu's theory of connections on graphs to define
a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are
generalizations of unitary connections. We show that this 2-category admits an
embedding into the 2-category of hyperfinite von Neumann algebras, generalizing
fundamental results from subfactor theory to a 2-categorical setting.
