From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/380 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: An introduction to n-categories Date: Thu, 15 May 1997 22:18:45 -0300 (ADT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016931 25505 80.91.229.2 (29 Apr 2009 14:55:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:31 +0000 (UTC) To: categories Original-X-From: cat-dist Thu May 15 22:20:37 1997 Original-Received: by mailserv.mta.ca; id AA08322; Thu, 15 May 1997 22:18:45 -0300 Original-Lines: 35 Xref: news.gmane.org gmane.science.mathematics.categories:380 Archived-At: Date: Tue, 13 May 1997 17:29:58 -0700 (PDT) From: john baez Here is the abstract of a paper that is now available in Postscript form at: http://math.ucr.edu/home/baez/ncat.ps If downloading it or printing it out is a problem, I can mail copies to people. ---------------------------------------------------------------------- An Introduction to n-Categories John C. Baez 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-category recently proposed by Dolan and the author.