From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9086 Path: news.gmane.org!.POSTED!not-for-mail From: David Roberts Newsgroups: gmane.science.mathematics.categories Subject: Reference for lifting an adjunction to a monoidal one Date: Sat, 28 Jan 2017 11:38:05 +1030 Message-ID: Reply-To: David Roberts NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: blaine.gmane.org 1485617434 23882 195.159.176.226 (28 Jan 2017 15:30:34 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 28 Jan 2017 15:30:34 +0000 (UTC) To: "categories@mta.ca list" Original-X-From: majordomo@mlist.mta.ca Sat Jan 28 16:30:30 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1cXUx9-0004Gd-0Y for gsmc-categories@m.gmane.org; Sat, 28 Jan 2017 16:30:11 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:53130) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cXUwN-00067g-0I; Sat, 28 Jan 2017 11:29:23 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cXUvw-0006ds-2K for categories-list@mlist.mta.ca; Sat, 28 Jan 2017 11:28:56 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9086 Archived-At: Hi all, I need a textbook or otherwise standard reference for the fact that if one has a pair of monoidal categories C, D, and an adjunction L -| R: UC <--> UD between their underlying categories, then if one of L or R lift to a (strong) monoidal functor, then the adjunction lifts to an adjunction in the 2-category of monoidal categories, strong monoidal functors and monoidal natural transformations. (Mac Lane of course only treats the case of strict monoidal functors, at least in my, older, edition of his book) Thanks, David [For admin and other information see: http://www.mta.ca/~cat-dist/ ]