From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2073 Path: news.gmane.org!not-for-mail From: maxk@maths.usyd.edu.au (Max Kelly) Newsgroups: gmane.science.mathematics.categories Subject: Re: Two categories or 2-categories? Date: Mon, 31 Dec 2001 19:55:56 +1100 (EST) Message-ID: <200112310855.fBV8tun306897@milan.maths.usyd.edu.au> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018384 2303 80.91.229.2 (29 Apr 2009 15:19:44 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:44 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Dec 31 10:55:44 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 31 Dec 2001 10:55:44 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16L3oB-0008DV-00 for categories-list@mta.ca; Mon, 31 Dec 2001 10:52:59 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 50 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:2073 Archived-At: I don't know quite what Peter's point is here: there is no difference between the spoken forms of "2-categories" and "two-categories". I think we all write "2-categories", as we write "n-categories" and "w-categories", where I am making-do with "w" for a lower-case Greek omega. Yet Blackwell, Power, and I, when we considered general questions about the algebras for 2-monads and the various kinds of strict and non-strict morphisms of these and some adjunctions between the 2-categories that arise, entitled our paper "Two-dimensional monad theory". I don't think "2-monad theory" would have represented our concerns as well, being capable of interpretation as meaning a wider study than ours, or a narrower one, depending on how it was taken by the reader. To the Australian Research Council, such work is described as research on two-dimensional universal algebra. What do others think? Regards - Max.