Computads, cellular sets, and multitopic sets
by
Michael Makkai
McGill University, Canada

This talk will report on joint work with Victor Harnik and Marek Zawadowski; a preliminary version of our paper can be seen at www.math.mcgill.ca/makkai/. There is more to the subject than what is explicitly stated in the paper at the present time (in fact, soon there is going to be a revised version of the paper, most likely in two independent parts). The adjunction between the category mltSet of multitopic sets and the category omegaCat, including the fact that the image of mltSet in omegaCat is exactly the category of many-to-one computads (a consequence of which is the fact that the category of many-to-one computads is a presheaf catregory), is now given a better presentation, which, besides being more economical, makes clear in an explicit manner the fact that the adjunction is monadic. On the other hand, the second half of the paper, which is not needed any more for purposes of the main theorem, is now seen as an analog of Michael Batanin's theory of the free omega category generated by an omega graph (globular set). Andre Joyal's cellular sets are related to Batanin's theory; I will propose the use of ``super-cellular sets'' which are a common extension of cellular sets and multitopic sets. Two particular consequences purely in terms of many-to-one computads are the fact that the word-problem for many-to-one computads is solvable, and that we have an elegant characterization of composable many-to-one computads.

Date received: September 10, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cajf-50.