An introduction to n-categories

[categories <cat-dist@mta.ca>]

Date: Tue, 13 May 1997 17:29:58 -0700 (PDT)
From: john baez <baez@math.ucr.edu>


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. 

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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.