From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7377 Path: news.gmane.org!not-for-mail From: Venkata Rayudu Posina Newsgroups: gmane.science.mathematics.categories Subject: Difference and Duality Date: Thu, 12 Jul 2012 15:03:16 +0430 Message-ID: Reply-To: Venkata Rayudu Posina NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1342288796 1393 80.91.229.3 (14 Jul 2012 17:59:56 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 14 Jul 2012 17:59:56 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sat Jul 14 19:59:56 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Sq6dH-0001Cw-MV for gsmc-categories@m.gmane.org; Sat, 14 Jul 2012 19:59:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:56366) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Sq6cD-00080S-N0; Sat, 14 Jul 2012 14:58:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Sq6cE-0000FU-JP for categories-list@mlist.mta.ca; Sat, 14 Jul 2012 14:58:50 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7377 Archived-At: Dear All, There is a contrast between a map with a section and a map with a retract: in the case of a map with a section we can find proof [of belonging]; and in the case of a map with a retract we find that there is one proof. The contrast appears a little more pronounced: in trying to show that there is one proof f of h in r in the case of a map r with a section s, the closest I got is srf1 = srf2; and in trying to find proof of 'h is in s' in the case of a map s with a retract r, the closest I got is srh. Is there a duality (knowing answer vs. knowing that there is one answer) in here? Please forgive me for rushing to ask for help if this is something that can become clear as I go through 'The contravariant parts functor' article (I'm still on the first page of the article in Conceptual Mathematics). Thank you, posina [For admin and other information see: http://www.mta.ca/~cat-dist/ ]