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.


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