announcement

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

Date: Thu, 3 Jul 1997 20:52:47 -0400 (EDT)
From: Michael Makkai <makkai@triples.math.mcgill.ca>

The following paper is announced:

		On weak higher dimensional categories

	by Claudio Hermida, Michael Makkai and John Power

Abstract: 

Inspired by the concept of opetopic set introduced in a recent paper by
John C. Baez and James Dolan, we give a modified notion called multitopic
set. The name reflects the fact that, whereas the Baez/Dolan concept is
based on operads, the one in this paper is based on multicategories. The
concept of multicategory used here is a mild generalization of the
same-named notion introduced by Joachim Lambek in 1969. Opetopic sets and
multitopic sets are both intended as vehicles for concepts of weak higher
dimensional category. Baez and Dolan define weak n-categories as
(n+1)-dimensional opetopic sets satisfying certain properties. The version
intended here, multitopic n-category, is similarly related to multitopic
sets. Multitopic n-categories are not described in the present paper; they
are to follow in a sequel. The present paper gives complete details of the
definitions and basic properties of the concepts involved in multitopic
sets. The category of multitopes, analogs of opetopes of Baez and Dolan,
is presented in full, and it is shown that the category of multitopic sets
is equivalent to the category of set-valued functors on the category of
multitopes. 



The paper is available by anonymous ftp from triples.math.mcgill.ca in
directory pub/makkai, or via the CRTC home page

	ftp://triples.math.mcgill.ca/crtc.html 

and click on "Makkai".  The paper is in nine files, each with a name
starting with `mult`; they are PostScript files. 

I will send a limited number of hard copies upon request.

Michael Makkai