From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5749 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Q. about monoidal functors Date: Thu, 06 May 2010 21:01:24 -0400 Message-ID: Reply-To: "Fred E.J. Linton" 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: dough.gmane.org 1273237029 9863 80.91.229.12 (7 May 2010 12:57:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 7 May 2010 12:57:09 +0000 (UTC) To: Steve Lack , categories Original-X-From: categories@mta.ca Fri May 07 14:57:05 2010 connect(): No such file or directory 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 4.69) (envelope-from ) id 1OAN73-00056y-E2 for gsmc-categories@m.gmane.org; Fri, 07 May 2010 14:57:05 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OAMai-0001UT-K6 for categories-list@mta.ca; Fri, 07 May 2010 09:23:40 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5749 Archived-At: Thanks, Steve, > Such a T is called a symmetric monoidal functor. Thanks for helping dispel my illusion that all monoidal functors might necessarily be thus symmetric :-) : = > Example: let _A_ be Set with the cartesian monoidal structure. Let > M be a monoid and let T be the functor Set->Set sending X to MxX (which= > I'll write as MX). This functor T is monoidal via the map MXMY->MXY sen= ding > (m,x,n,y) to (mn,x,y). It is symmetric monoidal iff M is commutative. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]