Computads and Multitopic Sets
  We compare computads with multitopic sets. Both these kinds of structures have n-dimensional objects (called n-cells and n-pasting diagrams, respectively). The computads form a subclass of the more familiar class of omega-categories, while multitopic sets have been devised by Hermida, Makkai and Power as a vehicle for a definition of the concepts of weak omega-category. Our main result states that the category of multitopic sets is equivalent to that of many-to-one computads, a certain full subcategory of the category of all computads. 
Victor Harnik, Michael Makkai and Marek Zawadowski