Pasting schemes for the monoidal biclosed structure on
-Cat
Chapter 3 of my Ph.D. thesis
``On combinatorial models for higher dimensional homotopies'',
1995, xxii+163+XV pp.
Abstract:
Using the theory of pasting presentations, developed in
chapter 2,
I give a detailed description of the tensor product on
-categories,
which extends Gray's tensor product on
2-categories and which is closely related to Brown-Higgins's tensor
product on -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
Utrecht
The Netherlands