From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6463 Path: news.gmane.org!not-for-mail From: Fernando Muro Newsgroups: gmane.science.mathematics.categories Subject: reference on enriched monoidal categories Date: Wed, 12 Jan 2011 08:50:03 +0100 Message-ID: Reply-To: Fernando Muro NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1294881367 20671 80.91.229.12 (13 Jan 2011 01:16:07 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 13 Jan 2011 01:16:07 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Thu Jan 13 02:16:03 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 1PdBnH-0000ld-LW for gsmc-categories@m.gmane.org; Thu, 13 Jan 2011 02:16:03 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:33368) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PdBn7-00072Y-Lh; Wed, 12 Jan 2011 21:15:53 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PdBn0-0005b9-Pn for categories-list@mlist.mta.ca; Wed, 12 Jan 2011 21:15:47 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6463 Archived-At: 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/ ]