From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/425 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: announcement Date: Thu, 3 Jul 1997 22:12:50 -0300 (ADT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016958 25696 80.91.229.2 (29 Apr 2009 14:55:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:58 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Jul 3 22:13:20 1997 Original-Received: by mailserv.mta.ca; id AA16333; Thu, 3 Jul 1997 22:12:50 -0300 Original-Lines: 45 Xref: news.gmane.org gmane.science.mathematics.categories:425 Archived-At: Date: Thu, 3 Jul 1997 20:52:47 -0400 (EDT) From: Michael Makkai 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