From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6469 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: reference on enriched monoidal categories Date: Fri, 14 Jan 2011 11:55:40 +1100 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1295032099 6753 80.91.229.12 (14 Jan 2011 19:08:19 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 14 Jan 2011 19:08:19 +0000 (UTC) Cc: categories@mta.ca To: Fernando Muro Original-X-From: majordomo@mlist.mta.ca Fri Jan 14 20:08:15 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Pdp0Q-0000J0-Re for gsmc-categories@m.gmane.org; Fri, 14 Jan 2011 20:08:15 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57764) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Pdp0H-0000V7-Ph; Fri, 14 Jan 2011 15:08:05 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Pdp0B-0007Yp-Vj for categories-list@mlist.mta.ca; Fri, 14 Jan 2011 15:08:00 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6469 Archived-At: Dear Fernando, I do not know of a discussion of the exact result you state, but much of what you need to prove it is in the appendix to: A Note on Actions of a Monoidal Category G. Janelidze and G.M. Kelly Theory and Applications of Categories, Vol. 9, 2001, No. 4, pp 61-91. Best wishes, Richard On 12 January 2011 18:50, Fernando Muro wrote: > Dear colleagues, > > I'm looking for a reference where the following fact (that I believe to > be clearly true) is discussed: > > Let V and C be biclosed monoidal categories. Suppose that V is symmetric > and that we have a strong braided monoidal functor z : V --> Z(C) to the > center of C in the sense of Joyal-Street. Assume further that the > functor z(-) \otimes Y : V --> C has a right adjoint Hom(Y,-) : C --> V > for any object Y in C. Then C is a monoidal V-category with Hom objects > in V given by this right adjoint. > > You may assume that V and C are (co)complete if you wish. > > It is easy to construct compositions morphisms, etc. in an elementary > way, but verifying all laws is a pain. This is why I'm willing to find a > reference. > > All the best for the new year, > > Fernando Muro [For admin and other information see: http://www.mta.ca/~cat-dist/ ]