From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4957 Path: news.gmane.org!not-for-mail From: "Reinhard Boerger" Newsgroups: gmane.science.mathematics.categories Subject: Famous unsolved problems in ordinary category theory Date: Tue, 9 Jun 2009 15:35:31 +0200 Message-ID: Reply-To: "Reinhard Boerger" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1244681976 8214 80.91.229.12 (11 Jun 2009 00:59:36 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 11 Jun 2009 00:59:36 +0000 (UTC) To: Original-X-From: categories@mta.ca Thu Jun 11 02:59:34 2009 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 4.50) id 1MEYdi-0008I5-4x for gsmc-categories@m.gmane.org; Thu, 11 Jun 2009 02:59:34 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MEY5J-0000GM-D5 for categories-list@mta.ca; Wed, 10 Jun 2009 21:24:01 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4957 Archived-At: Dear categorists, When I read the question for the first time, I did not know such a = problem. Moreover, my impression was that in category theory one often finds new results, which had not been conjectured before. Sometimes an important = part of the work is even to develop the right notions. This may explain that there are less important well-known problems in category theory than in other areas. Nevertheless, I remember a problem that can be easily formulated in pure category and is still unsolved as far as I know. Bur it does not seem = vastly distributed. Cantor's diagonal says that says that the power set always = is of larger cardinality as the original set. Gavin Wraith suggested the following generalization to topoi: If for two objects A,B there is a monomorphism A^B>->B, is there also a monomorphism A>->1? This looks = like a meaningful analogue, and I have not seen an answer in the meantime. The question can even be asked not only in a topos, but in every cartesian closed category. Does anybody know anything about progress? Greetings Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]