From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4949 Path: news.gmane.org!not-for-mail From: Hasse Riemann Newsgroups: gmane.science.mathematics.categories Subject: =?windows-1256?Q?Famous_uns?= =?windows-1256?Q?olved_prob?= =?windows-1256?Q?lems_in_or?= =?windows-1256?Q?dinary_cat?= =?windows-1256?Q?egory_theo?= =?windows-1256?Q?ry=FE?= Date: Mon, 8 Jun 2009 01:34:10 +0000 Message-ID: Reply-To: Hasse Riemann NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="windows-1256" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1244483208 28817 80.91.229.12 (8 Jun 2009 17:46:48 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 8 Jun 2009 17:46:48 +0000 (UTC) To: Category mailing list Original-X-From: categories@mta.ca Mon Jun 08 19:46:44 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 1MDivY-0007Rt-NY for gsmc-categories@m.gmane.org; Mon, 08 Jun 2009 19:46:32 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MDiOt-0007bT-VL for categories-list@mta.ca; Mon, 08 Jun 2009 14:12:48 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:4949 Archived-At: =20 Hi categorists =20 OK, here is the beuty of collecting and spreading problems that many seem= to miss. It just took me a few days to change my mood from the depressing answers not to look for problems. Again i am much more for structuring of mathema= tics. =20 Usually you only get to know what is proved and not what is unproved. Problems complete this by letting you know what to not to look for. They also answer your questions even if it is by saying unkown or a conje= cture. Then, on the other hand, they are good research projects so they should b= e widely known. Just maby someone undertakest them and happens to find the solution. But often he must first see the problem. =20 The problems Ross Street put forward are so beautiful i have decided to p= ost 2 problems i have learned from him, unedited. =20 1) Fermat's Last Theorem is about the category of finite sets. Is there a ca= tegorical proof? Can we characterize those categories C in which x^n + y^n isomorphic to z= ^n has only trivial solutions for n> 2? =20 2) The category of finite sets is a concrete form of the set N of natural nu= mbers. What are concrete forms of Z, Q, R and C? If anyone know some problems of these sort below let me know. =20 * characterization problems * inherit properties problems * every category/functor/... of type A is a category/functor/... of type = B =20 =20 I also foregot to mention before that i know and more than like Grothendi= ecks philosophy of dissolving problems by developing a proper framework for rhem. =20 Best regards Rafael Borowiecki [For admin and other information see: http://www.mta.ca/~cat-dist/ ]