From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5199 Path: news.gmane.org!not-for-mail From: robin@ucalgary.ca Newsgroups: gmane.science.mathematics.categories Subject: Conditions for adjoints -- another variant Date: Sat, 24 Oct 2009 17:11:26 -0600 (MDT) Message-ID: Reply-To: robin@ucalgary.ca 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: ger.gmane.org 1256432155 27341 80.91.229.12 (25 Oct 2009 00:55:55 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 25 Oct 2009 00:55:55 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sun Oct 25 02:55:48 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 1N1rOd-0007m7-6L for gsmc-categories@m.gmane.org; Sun, 25 Oct 2009 02:55:47 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N1qqu-0002HW-4J for categories-list@mta.ca; Sat, 24 Oct 2009 21:20:56 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5199 Archived-At: BTW. Here are some even cleaner conditions .... There is an adjoint between two categories iff there are two object functions F and G (not required to be functors) and For each X \in \X and Y \in \Y there are two functions: #: \X(X,G(Y)) -> \Y(F(X),Y) ---- sharp @: \Y(F(X),Y) -> \X(X,G(Y)) ---- flat (i)' @ and # are inverse @(#(f)) =3D f and #(@(g)) =3D g (ii)' @(h k) =3D @(h) @(#(1) k) and dually #(xy) =3D #(x @(1)) #(y) Still hoping to find where these all are recorded!! -robin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]