Pasting schemes for the monoidal biclosed structure on omega-Cat

Chapter 3 of my Ph.D. thesis ``On combinatorial models for higher dimensional homotopies'', 1995, xxii+163+XV pp.


Using the theory of pasting presentations, developed in chapter 2, I give a detailed description of the tensor product on omega-categories, which extends Gray's tensor product on 2-categories and which is closely related to Brown-Higgins's tensor product on omega-groupoids. Immediate consequences are a general and uniform definition of higher dimensional lax natural transformations, and a nice and transparent description of the corresponding internal homs. Further consequences will be in the development of a theory for weak n-categories, since both tensor products and lax structures are crucial in this.

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Sjoerd E. Crans
Mathematical Institute
Utrecht University
The Netherlands