From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6152 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Dual of a monoidal closed category Date: Mon, 13 Sep 2010 10:19:19 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1284402657 21120 80.91.229.12 (13 Sep 2010 18:30:57 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 13 Sep 2010 18:30:57 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Mon Sep 13 20:30:56 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OvDnr-0007bf-5B for gsmc-categories@m.gmane.org; Mon, 13 Sep 2010 20:30:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:49391) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OvDmX-0006n8-6i; Mon, 13 Sep 2010 15:29:33 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OvDmQ-0000Gk-MG for categories-list@mlist.mta.ca; Mon, 13 Sep 2010 15:29:26 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6152 Archived-At: Is it common knowledge that the dual of a monoidal closed category is also monoidal closed (at least in the symmetric case, but I don't think that matters). If you denote tensor by @ and hom by --o, then define a dual hom by A --x B = (A* --o B*)* and a dual tensor by A # B = (A* @ B*)* where * is the contravariant equivalence. The proof that this works is trivial. What it means is another matter entirely. Right now, I just would like to know if this is commonly known. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]