From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4198 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: Re: question about monoidal categories Date: Fri, 8 Feb 2008 09:31:58 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019788 12182 80.91.229.2 (29 Apr 2009 15:43:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:43:08 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Feb 8 15:00:05 2008 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Feb 2008 15:00:05 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JNYOU-0004YU-Ji for categories-list@mta.ca; Fri, 08 Feb 2008 14:56:14 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 20 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:4198 Archived-At: Dear Paul, Let us forget about the monoidal unit and fix (a). You define a strict semi? monoidal structure on S letting x*y = x. Then your pair (F, beta) is a lax monoidal functor M --> S. Your condition (a) is the hexagon of consistency with alpha, which here reduces to: F(p) = F(p) || | F(p) F(p*a) | | F(p*(a*b) --> F((p*a)*b) (a single | stands for a downward beta) Now, to fix also (b), I guess you should add to S a new object which is a strict identity for the tensor and work out things. However, if your problem is only about terminology and you do not want to use the tensor on S in the sequel (eg to compose F with other monoidal functors), you might not bother about that. Best regards Marco