2000/11/16 by Tom Leinster, Leinster, Tom
Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AT #math.CT #math.QA
paper · pdf · doi:10.48550/arxiv.math/0011106
viii + 127 pages
arxiv created 2000/11/16 · arxiv updated 2009/11/30
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.