From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5664 Path: news.gmane.org!not-for-mail From: Mark Spezzano Newsgroups: gmane.science.mathematics.categories Subject: Are there exactly 11 categories with 3 arrows? Date: Sat, 27 Mar 2010 00:37:31 +1030 Message-ID: Reply-To: Mark Spezzano NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1077) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1269649906 10104 80.91.229.12 (27 Mar 2010 00:31:46 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 27 Mar 2010 00:31:46 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Mar 27 01:31:41 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 1NvJwC-0004pC-Qs for gsmc-categories@m.gmane.org; Sat, 27 Mar 2010 01:31:41 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NvJSF-0007ZI-6c for categories-list@mta.ca; Fri, 26 Mar 2010 21:00:43 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5664 Archived-At: Hi, This is a beginner's question. I have a textbook (Walters) that asks to = show that there are exactly 11 categories with 3 arrows. Now, my logic tells me that I need to cover three possibilities: a) One object with three arrows. How many are there of these? b) Two objects with three arrows. How many are there of these? c) Three objects with three arrows. I think that the answer to this is = the easiest. The answer is 1 categories because they are all = endomorphisms, each object containing just the identity morphism. So the other 10 arrows must come from a) and b), but I keep getting = different answers like 12 and 13 categories as the total. Can someone please explain to me the combinations of categories that = need to be covered and why some are missed out during the calculation. Any help would be immensely appreciated. Thanks, Mark Spezzano= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]