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 ---------------------------------------------------------------------- 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. ----------------------------------------------------------------------- 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