From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5748 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Q. about monoidal functors Date: Thu, 06 May 2010 02:01:10 -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 1273186149 17280 80.91.229.12 (6 May 2010 22:49:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 6 May 2010 22:49:09 +0000 (UTC) To: Original-X-From: categories@mta.ca Fri May 07 00:49:06 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 1OA9sM-0003Vd-FZ for gsmc-categories@m.gmane.org; Fri, 07 May 2010 00:49:02 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OA9N6-0005nd-8w for categories-list@mta.ca; Thu, 06 May 2010 19:16:44 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5748 Archived-At: Suppose _A_ is a symmetric monoidal category in the sense of the Eilenberg-Kelley La Jolla paper, and T: _A_ --> _A_ a monoidal functor. What, if anything, is known, where τ: X ⊗ Y --> Y ⊗ X is the symmetry structure on the (symmetric) tensor product ⊗, = as to whether [T_X,Y: TX ⊗ TY --> T(X ⊗ Y)] = and = [T(τ_X,Y): T(X ⊗ Y) --> T(Y ⊗ X)] have the same composition as have [τ_TX,TY: TX ⊗ TY --> TY ⊗ TX] and [T_Y,X: TY ⊗ TX --> T(Y ⊗ X)] ? TIA for any relevant information and/or references thereto. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]