From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/21 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Symmetric monoidal closed natural transformation? Date: Fri, 30 Jan 2009 10:09:34 -0800 Message-ID: Reply-To: Mike Stay NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1233341071 14745 80.91.229.12 (30 Jan 2009 18:44:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 30 Jan 2009 18:44:31 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Fri Jan 30 19:45:44 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 1LSyN0-0006x3-H5 for gsmc-categories@m.gmane.org; Fri, 30 Jan 2009 19:45:38 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LSxwE-0002TC-Ek for categories-list@mta.ca; Fri, 30 Jan 2009 14:17:58 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:21 Archived-At: On Thu, Jan 29, 2009 at 7:05 PM, Mike Stay wrote: > A symmetric monoidal functor F:C->D is closed if the morphism > c_D(Phi_{x -o y, x}^{-1} o F(c_C^{-1}(1_{x -o y}))):F(x -o y) -> F(x) -o F(y) > is an isomorphism, where x,y in C, > Phi_{x,y}:F(x) tensor F(y) -> F(x tensor y) > and c_C and c_D are currying in C, D. > > Could someone give me the definition of a symmetric monoidal closed > natural transformation? I thought it would be a simple commuting > diagram like the one involving Phi, but one of the arrows goes the > wrong way. Thanks to all those who responded, letting me know that precisely because of the arrow going the "wrong" way, it only makes sense to talk about symmetric monoidal closed natural isomorphisms. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com