Computads and Multitopic Sets

Details Computads and Multitopic Sets Computads and Multitopic Sets

2008-11-20

arxiv.org/abs/0811.3215v1

Mathematics

Category Theory

53 pages, references added

Scientific paper

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.

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