Categorification

Categorification

[categories]

Date: Sat, 7 Feb 1998 16:00:14 -0800 (PST)
From: john baez <baez@math.ucr.edu>


Here is the abstract of a paper that is now available at my website.

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Categorification 

John C. Baez and James Dolan

To appear in Proceedings of the Workshop on Higher Category Theory 
and Mathematical Physics at Northwestern University, Evanston, Illinois,
March 1997, eds. Ezra Getzler and Mikhail Kapranov.

Categorification is the process of finding category-theoretic analogs of
set-theoretic concepts by replacing sets with categories, functions with
functors, and equations between functions by natural isomorphisms
between functors, which in turn should satisfy certain equations of
their own, called `coherence laws'.   Iterating this process requires a
theory of `n-categories', algebraic structures having objects,
morphisms between objects, 2-morphisms between morphisms and so on up to
n-morphisms.  After a brief introduction to n-categories and their
relation to homotopy theory, we discuss algebraic structures that can be
seen as iterated categorifications of the natural numbers and integers.
These include tangle n-categories, cobordism n-categories, and the homotopy 
n-types of the loop spaces Omega^k S^k.  We conclude by describing a 
definition of weak n-categories based on the theory of operads.

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The paper is available in Postscript form on the web at

http://math.ucr.edu/home/baez/cat.ps

I can also email or snailmail you a copy at your request.