  In this paper, we explain how the classical Catalan families of objects
involving paths, tableaux, triangulations, parentheses configurations and more
generalize canonically to a three-dimensional version. In particular, we
present product-coproduct prographs as central objects explaining the
combinatorics of the triangulations of the sphere. Then we expose a natural way
to extend the Tamari lattice to the product-coproduct prographs.
