Structures in higher-dimensional category theory
摘要
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 Chapters I and II, which cover this theory and its application to give a definition of weak n-category, are largely superseded by my thesis (math.CT/0011106), but Chapters III and IV have not appeared elsewhere.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.
引用
@article{arxiv.math/0109021,
title = {Structures in higher-dimensional category theory},
author = {Tom Leinster},
journal= {arXiv preprint arXiv:math/0109021},
year = {2007}
}
备注
81 pages, written 1998