From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/540 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Big Omega available Date: Thu, 27 Nov 1997 16:01:49 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241017025 26197 80.91.229.2 (29 Apr 2009 14:57:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:05 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Nov 27 16:06:21 1997 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA05940; Thu, 27 Nov 1997 16:01:50 -0400 (AST) X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by mailserv.mta.ca id QAA05940 Original-Lines: 43 Xref: news.gmane.org gmane.science.mathematics.categories:540 Archived-At: Date: Thu, 27 Nov 1997 10:31:13 +1100 From: Ross Street Dear Colleagues This is to announce the availability at http://www-math.mpce.mq.edu.au/~mbatanin/Bigomega.ps of a short 10 page note which begins as follows: ********************************************************************** "The universal property of the multitude of trees" Michael Batanin and Ross Street Macquarie University, N S W 2109 AUSTRALIA Email and November 1997 Lawvere [BL] essentially pointed out that the category Delta, whose objects are finite ordinals and whose arrows are order-preserving functions, is the generic monoidal category containing a monoid. Let Mon be the category of monoids in the category Set of sets. Bénabou [Be] pointed out that the (simplicial) nerve of the category Delta is the standard resolution [BB] of the terminal monoid via the comonad generated by the underlying functor Mon --> Set and its left adjoint. Let Omcat denote the category of omega-categories and let Glob denote the category of globular sets. In this note we announce a generic property of the category BigOmega whose nerve is the standard resolution of the terminal omega-category via the comonad generated by the underlying functor Omcat --> Glob and its left adjoint. We also give a concrete model for BigOmega in terms of trees. Furthermore, we make connections with the recent work of Joyal [J]. Full proofs of our claims will appear elsewhere. ************************************************************************** Regards, Michael Batanin and Ross Street