Pasting presentations for omega-categories

Chapter 2 of my Ph.D. thesis ``On combinatorial models for higher dimensional homotopies'', 1995, xxii+163+XV pp.

Abstract:

The pasting theorem showed that pasting schemes are useful in studying free omega-categories. It was thought that their inflexibility with respect to composition and identities prohibited wider use. This is not the case: there is a way of dealing with identities which makes it possible to describe omega-categories in terms of generating pasting schemes and relations between generated pastings, i.e., with pasting presentations. In this chapter I develop the necessary machinery for this. The main result, that the omega-category generated by a pasting presentation is universal with respect to respectable families of realizations, is a generalization of the pasting theorem.

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Sjoerd E. Crans
Mathematical Institute
Utrecht University
Utrecht
The Netherlands