The following paper is available at www.math.mcgill.ca/makkai/ Multitopic sets are the same as many-to-one computads by V. Harnik (University of Haifa), M. Makkai (McGill University) and M. Zawadowski (University of Warsaw) Abstract: For the definition of "computad", a concept due to Ross Street, see [M. A. Batanin, Computads for Finitary Monads on Globular Sets, AMS Contemporary Mathematics 230 (1998), pp. 37-57]. A "many-to-one" computad is one in which the codomain of each generating cell of positive dimension is itself a generating cell. For the concept of "multitopic set", see [C. Hermida, M. Makkai, J. Power, On weak higher dimensional categories I-3, JPAA 166 (2002), 83-104]. In the present paper, we prove the Theorem. The category of multitopic sets is equivalent to the category of many-to-one computads. 13-Jun-2002 15:39:17 -0300,6729;000000000000-00000000