  A Morse 2-function is a generic smooth map from a smooth manifold to a
surface. In the absence of definite folds (in which case we say that the Morse
2-function is indefinite), these are natural generalizations of broken
(Lefschetz) fibrations. We prove existence and uniqueness results for
indefinite Morse 2-functions mapping to arbitrary compact, oriented surfaces.
"Uniqueness" means there is a set of moves which are sufficient to go between
two homotopic indefinite Morse 2-functions while remaining indefinite
throughout. We extend the existence and uniqueness results to indefinite, Morse
2-functions with connected fibers.
