From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/56 Path: news.gmane.org!not-for-mail From: Tony Meman Newsgroups: gmane.science.mathematics.categories Subject: symmetric monoidal adjunctions Date: Mon, 9 Feb 2009 12:26:32 +0100 Message-ID: Reply-To: Tony Meman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1234207271 5525 80.91.229.12 (9 Feb 2009 19:21:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 9 Feb 2009 19:21:11 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Mon Feb 09 20:22:26 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1LWbhz-0001Ot-9l for gsmc-categories@m.gmane.org; Mon, 09 Feb 2009 20:22:19 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LWbDR-0004d2-5V for categories-list@mta.ca; Mon, 09 Feb 2009 14:50:45 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:56 Archived-At: Dear category theorists, I have a question concerning symmetric monoidal adjunctions (of symmetric monoidal functors). Let V and W be symmetric monoidal categories, C a small category, F, G symmetric monoidal functors and F:V<-->W:G a symmetric monoidal adjunction. Is f:Fun(C,V)<-->Fun(C,W):g a symmetric monoidal adjunction? The functor categories Fun(C,V) and Fun(C,W) are endowed with the pointwise symmetric monoidal structure and the functors f and g are defined pointwise, too. I am sorry that I have to ask you all this things about monoidal categories and enriched categories but I can't find a book on that. I would be very pleased if anybody can suggest me something to read. Thank you in advance for any help. Tony