Higher-dimensional paper available

Higher-dimensional paper available

[Tom Leinster]

Higher-dimensional paper available, from

http://www.dpmms.cam.ac.uk/~leinster.


		Structures in Higher-Dimensional Category Theory

This is an exposition of some of the constructions which have arisen in
higher-dimensional category theory. We start with a review of the general
theory of operads and multicategories. Using this we give an account of
Batanin's definition of n-category; we also give an informal definition in
pictures. Next we discuss Gray-categories and their place in coherence
problems. Finally, we present various constructions relevant to the opetopic
definitions of n-category.

New material includes a suggestion for a definition of lax cubical
n-category; a characterization of small Gray-categories as the small
substructures of 2-Cat; a conjecture on coherence theorems in higher
dimensions; a construction of the category of trees and, more generally, of
n-pasting diagrams; and an analogue of the Baez-Dolan slicing process in the
general theory of operads.


(A few corrections have been made to the version of this distributed at the
PSSL in Utrecht, and these are listed at the web site.)


Tom Leinster