From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8977 Path: news.gmane.org!.POSTED!not-for-mail From: Robert Pare Newsgroups: gmane.science.mathematics.categories Subject: Re: Half cartesian duoical categories Date: Sat, 8 Oct 2016 11:31:18 +0000 Message-ID: References: Reply-To: Robert Pare NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1476035104 27570 195.159.176.226 (9 Oct 2016 17:45:04 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sun, 9 Oct 2016 17:45:04 +0000 (UTC) Cc: "categories@mta.ca" , Marco Grandis To: David Yetter Original-X-From: majordomo@mlist.mta.ca Sun Oct 09 19:44:57 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.28]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1btI9V-0004ur-Ox for gsmc-categories@m.gmane.org; Sun, 09 Oct 2016 19:44:45 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52936) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1btI9I-0007H7-Tb; Sun, 09 Oct 2016 14:44:32 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1btI97-0001ZY-29 for categories-list@mlist.mta.ca; Sun, 09 Oct 2016 14:44:21 -0300 Thread-Topic: categories: Half cartesian duoical categories Thread-Index: AQHSIMuTJ9phghk7GEKrX4FiaHgCZqCebV6A In-Reply-To: Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8977 Archived-At: Hi David, You'll find a lot of information on this sort of duoidal category and varia= tions thereon in our paper "Intercategories: a framework for three-dimensional category theory" = available as #53 at http://www.mscs.dal.ca/~pare/publications.html though there is no special name given for it there (as you were asking). Bob (&Marco) On 2016-10-06, at 4:48 PM, David Yetter wrote: > Is there already a name in the literature for the special instance of duo= idal category in which one of the monoidal structures is cartesian? In par= ticular the instance in which if # denotes the non-cartesian monoidal struc= ture and x the cartesian, the lax middle-four interchange transformation ha= s components >=20 >=20 > (A x B) # (C x D) ------> (A # B) x (C # D) ? >=20 >=20 > It has come up in my current student's dissertation work. An existing na= me and citations to papers using this specific type of duoidal category wo= uld be much appreciated. >=20 >=20 > Best Thoughts, >=20 > David Yetter >=20 > Professor of Mathematics >=20 > Kansas State University >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]