From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3830 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Actions of monoidal functors [was Re: Arens product] Date: Thu, 19 Jul 2007 14:46:41 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.2) Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019549 10498 80.91.229.2 (29 Apr 2009 15:39:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:09 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Fri Jul 20 17:04:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 20 Jul 2007 17:04:37 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IByZ6-0002pt-Ow for categories-list@mta.ca; Fri, 20 Jul 2007 16:55:04 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 24 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:3830 Archived-At: Dear Jeff "Monoid" and "object on which a monoid acts" make sense in any multicategory. A monoidal functor is a monoid in the convolution multicategory [V,W] of functors from V to W. The T of which you speak is an object on which M acts in [V,W]. Regards, Ross On 18/07/2007, at 4:11 AM, Jeff Egger wrote: > In general, given a monoidal functor M:V-->W and a functor T:V-->W, a > right-action of M on T should be a n.t. of the form T(A)@M(B)-->T(A@B) > satisfying the obvious associativity and unitality axioms. > -------------------- > I have always assumed that this concept is well-known, but I haven't > succeeded in finding a reference in the literature for it... perhaps > some of the more well-read readers of this list could help me out?