From: Tom Holroyd Subject: Re: on beyond exponentiation Date: Mon, 27 Dec 1999 18:08:26 +0900 Newsgroups: sci.math Keywords: n-categories On Wed, 22 Dec 1999, Tom Holroyd wrote: > Relatedly, we also have that morphisms of objects are called arrows, and > these together make up categories. Morphisms of categories are called > functors, and morphisms of functors are called natural transformations. > What about morphisms of natural transformations? Do they exist? Are they > different? It turns out that there are things called n-categories, where n says how many times you iterate this. Thus 1-categories are ordinary categories, 2-categories have 2-morphisms (which are morphisms of morphisms) and 3- categories have 3-morphisms, and so on. Hit the link below for a good place to start. http://math.ucr.edu/home/baez/week49.html It seems that this sort of thing may have applications in theoretical physics, where it is being used to describe quantum field theories, string theory, and other attempts at grand unification.