From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4196 Path: news.gmane.org!not-for-mail From: Paul B Levy Newsgroups: gmane.science.mathematics.categories Subject: question about monoidal categories Date: Thu, 7 Feb 2008 20:05:47 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019787 12171 80.91.229.2 (29 Apr 2009 15:43:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:43:07 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Feb 7 17:22:21 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 07 Feb 2008 17:22:21 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JNDzY-0003pl-Hj for categories-list@mta.ca; Thu, 07 Feb 2008 17:09:08 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:4196 Archived-At: Let F be a functor from a monoidal category M to a category S. We are given beta(p,a) : F(p) --> F(p*a) natural in p,a in M. If I tell you that, in addition to naturality, beta is "monoidal", I'm sure you will immediately guess what I mean by this, viz. (a) for any p,a,b in M beta(p,a) ; beta(p*a,b) = beta(p,a*b) ; F(alpha(p,a,b)) (b) for any p in M beta(p,1) = F(rho(p)) Yet I cannot see any reason for giving the name "monoidality" to (a)-(b). It doesn't appear to be a monoidal natural transformation in the official sense. There are no monoidal functors in sight. Can somebody please justify my usage? Paul