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Structures in higher-dimensional category theory

Tom Leinster
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Abstract

This paper, written in 1998, aims to clarify various higher categorical structures, mostly through the theory of generalized operads and multicategories. Chapters I and II, which cover this theory and its application to give a definition of weak n-category, are largely superseded by my thesis (math.CT/0011106), but Chapters III and IV have not appeared elsewhere. The main result of Chapter III is that small Gray-categories can be characterized as the sub-tricategories of the tricategory of 2-categories, homomorphisms, strong transformations and modifications; there is also a conjecture on coherence in higher dimensions. Chapter IV defines opetopes and a category of n-pasting diagrams for each n, which in the case n=2 is a definition of the category of trees.

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Tom Leinster. 2001-09-04. Structures in higher-dimensional category theory. https://arxiv.org/abs/math/0109021

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