From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7828 Path: news.gmane.org!not-for-mail From: "Harley D. Eades III" Newsgroups: gmane.science.mathematics.categories Subject: Non-triviality of *-autonomous categories Date: Sat, 3 Aug 2013 19:06:30 -0500 Message-ID: <77BE9A54-A589-408D-89B0-9C99D20B7F45@gmail.com> Reply-To: "Harley D. Eades III" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Mac OS X Mail 6.2 \(1499\)) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1375623034 31435 80.91.229.3 (4 Aug 2013 13:30:34 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 4 Aug 2013 13:30:34 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Aug 04 15:30:37 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1V5yOK-0005g7-Rw for gsmc-categories@m.gmane.org; Sun, 04 Aug 2013 15:30:36 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58389) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1V5yMi-0000EO-ES; Sun, 04 Aug 2013 10:28:56 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1V5yMh-000756-H6 for categories-list@mlist.mta.ca; Sun, 04 Aug 2013 10:28:55 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7828 Archived-At: Hi, everyone. =20 I am having trouble finding a reference. I thought perhaps someone here might know. It is well known that adding the isomorphism: d : A -> (A =3D> 1) =3D> 1 to a bicartisan closed category degenerates to a preorder. In *-autonomous categories we have such an isomorphism, but is non-trivial. Where can I find a proof of this? I would like to reference it. =20 I think one could proof this using the category of coherence spaces and = linear maps as a concrete *-autonomous category. See for example: [1] R. a. g. Seely. Linear logic, *-autonomous categories and cofree = coalgebras. In Computer Science Logic, 1989. Any references anyone might have would be great. =20 Thanks, .\ Harley [For admin and other information see: http://www.mta.ca/~cat-dist/ ]