#
Operads in higher-dimensional category theory

##
Tom Leinster

The purpose of this paper is to set up a theory of generalized operads and
multicategories and to use it as a language in which to propose a definition of weak
n-category. Included is a full explanation of why the proposed definition of
n-category is a reasonable one, and of what happens when n is less than or equal to
2. Generalized operads and multicategories play other parts in higher-dimensional
algebra too, some of which are outlined here: for instance, they can be used to
simplify the opetopic approach to n-categories expounded by Baez, Dolan and others,
and are a natural language in which to discuss enrichment of categorical structures.

Keywords:
n-category, operad, higher-dimensional category

2000 MSC:
18D05, 18D50, 18F99, 18A99

*Theory and Applications of Categories,*
Vol. 12, 2004,
No. 3, pp 73-194.

http://www.tac.mta.ca/tac/volumes/12/3/12-03.dvi

http://www.tac.mta.ca/tac/volumes/12/3/12-03.ps

http://www.tac.mta.ca/tac/volumes/12/3/12-03.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/3/12-03.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/3/12-03.ps

TAC Home