weak n-categories

weak n-categories

[categories]

Date: Wed, 5 Feb 1997 15:10:25 -0800 (PST)
From: john baez <baez@charity.ucr.edu>

Here is the abstract of a paper that is now available at my website.
If printing it out is a problem (see below) I can mail copies to
people. - John Baez

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Higher-Dimensional Algebra III:
n-Categories and the Algebra of Opetopes

John C. Baez and James Dolan

We give a definition of weak n-categories based on the theory of
operads.  We work with operads having an arbitrary set S of types, or
`S-operads', and given such an operad O, we denote its set of
operations by elt(O).  Then for any S-operad O there is an
elt(O)-operad O+ whose algebras are S-operads over O.  Letting I be
the initial operad with a one-element set of types, and defining I(0)
= I, I(i+1) = I(i)+, we call the operations of I(n-1) the
`n-dimensional opetopes'.  Opetopes form a category, and presheaves on
this category are called `opetopic sets'.  A weak n-category is
defined as an opetopic set with certain properties, in a manner
reminiscent of Street's simplicial approach to weak omega-categories.
In a similar manner, starting from an arbitrary operad O instead of I,
we define `n-coherent O-algebras', which are n times categorified
analogs of algebras of O.  Examples include `monoidal n-categories',
`stable n-categories', `virtual n-functors' and `representable
n-prestacks'.  We also describe how n-coherent O-algebra objects may
be defined in any (n+1)-coherent O-algebra.
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The paper is available in Postscript form on the web at

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

The paper is 59 pages long, so this file is rather large.  
A compressed version is available at

http://math.ucr.edu/home/baez/op.ps.Z

You can download this and then (on most UNIX systems) type

uncompress op.ps.Z

to get the Postscript file.

If you like ftp, you can also get these by anonymous
ftp to 

math.ucr.edu

They are in the directory

pub/baez

as the files op.ps and op.ps.Z