From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8097 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: "Weakly closed" monoidal bicategories? Date: Sat, 03 May 2014 10:36:08 +1000 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1399210030 5554 80.91.229.3 (4 May 2014 13:27:10 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 4 May 2014 13:27:10 +0000 (UTC) To: Mike Stay , categories Original-X-From: majordomo@mlist.mta.ca Sun May 04 15:27:05 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1WgwRY-0005AE-7m for gsmc-categories@m.gmane.org; Sun, 04 May 2014 15:27:00 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44095) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1WgwQQ-0002Uf-7l; Sun, 04 May 2014 10:25:50 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1WgwQO-00027F-CO for categories-list@mlist.mta.ca; Sun, 04 May 2014 10:25:48 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8097 Archived-At: Dear Mike, This paper of Vincent Schmitt involves such a structure on the 2-category of symmetric monoidal categories. I don't think the abstract structure of which this is an instance is made explicit though. http://arxiv.org/abs/0711.0324 Richard On Sat, May 3, 2014, at 01:40 AM, Mike Stay wrote: > In a closed symmetric monoidal bicategory, the categories > Hom(A tensor B, C) > and > Hom(A, hom(B, C)) > are equivalent. It occurred to me that one could weaken this > equivalence to a mere adjunction. Looking for references, I found > Lars Birkedal's thesis where he considers "weakly closed partial > cartesian" bicategories. > > Are there other references I should be aware of? Thanks! > -- > Mike Stay - metaweta@gmail.com > http://www.cs.auckland.ac.nz/~mike > http://reperiendi.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]