Operads in higher-dimensional category theory

Leinster, T. (2004) Operads in higher-dimensional category theory. Theory and Applications of Categories, 12(3), pp. 73-194.

Abstract

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Leinster, Dr Tom
• Authors: Leinster, T.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Theory and Applications of Categories
• ISSN (Online): 1201-561X

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