An Introduction to n-Categories
摘要
An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of n-category, with an emphasis on `weak' n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence. (An n-morphism is an equivalence if it is invertible, while a j-morphism for j < n is an equivalence if it is invertible up to a (j+1)-morphism that is an equivalence.) We discuss applications of weak n-categories to various subjects including homotopy theory and topological quantum field theory, and review the definition of weak n-categories recently proposed by Dolan and the author.
引用
@article{arxiv.q-alg/9705009,
title = {An Introduction to n-Categories},
author = {John C. Baez},
journal= {arXiv preprint arXiv:q-alg/9705009},
year = {2008}
}
备注
34 pages LaTeX, 30 encapsulated Postscript figures, 2 style files