Operads in Higher-Dimensional Category Theory

Tom Leinster

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Operads in Higher-Dimensional Category Theory

Tom Leinster

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Abstract

The purpose of this dissertation 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=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.

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BibTeX RIS

Tom Leinster. 2000-11-16. Operads in Higher-Dimensional Category Theory. https://arxiv.org/abs/math/0011106

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