From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5667 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Are there exactly 11 categories with 3 arrows? Date: Fri, 26 Mar 2010 22:03:30 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1269720852 1066 80.91.229.12 (27 Mar 2010 20:14:12 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 27 Mar 2010 20:14:12 +0000 (UTC) To: Mark Spezzano , Original-X-From: categories@mta.ca Sat Mar 27 21:14:07 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1NvcOV-0000qB-39 for gsmc-categories@m.gmane.org; Sat, 27 Mar 2010 21:14:07 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Nvbri-0005wN-AY for categories-list@mta.ca; Sat, 27 Mar 2010 16:40:14 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5667 Archived-At: On Fri, 26 Mar 2010, at 08:09:06 PM EDT, Mark Spezzano asked: = > Are there exactly 11 categories with 3 arrows? Some gentle hints, without giving away the answers: > ... I need to cover three possibilities: > = > a) One object with three arrows. How many are there of these? That's the heart of the problem: how many monoid structures can be imposed on the identity and the two non-identity arrows? = > b) Two objects with three arrows. How many are there of these? Where can the single non-identity arrow be? = > c) Three objects with three arrows. ... the answer to this ... is 1 ...= Agreed. HTH. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]