From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8976 Path: news.gmane.org!.POSTED!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Half cartesian duoical categories Date: Sat, 8 Oct 2016 02:57:04 +0000 Message-ID: References: Reply-To: Ross Street NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1476035004 15759 195.159.176.226 (9 Oct 2016 17:43:24 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sun, 9 Oct 2016 17:43:24 +0000 (UTC) Cc: "categories@mta.ca list" To: David Yetter Original-X-From: majordomo@mlist.mta.ca Sun Oct 09 19:43:12 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 1btI7t-0001n5-Gx for gsmc-categories@m.gmane.org; Sun, 09 Oct 2016 19:43:05 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52930) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1btI7g-00072O-6B; Sun, 09 Oct 2016 14:42:52 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1btI7U-0001XN-Aq for categories-list@mlist.mta.ca; Sun, 09 Oct 2016 14:42:40 -0300 In-Reply-To: Accept-Language: en-GB, en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8976 Archived-At: Dear David On 7 Oct 2016, at 6:48 AM, David Yetter > wrote: In particular the instance in which if # denotes the non-cartesian monoida= l structure and x the cartesian, the lax middle-four interchange transforma= tion has components (A x B) # (C x D) ------> (A # B) x (C # D) ? You mean, of course, (A x B) # (C x D) ------> (A # C) x (B # D) It has come up in my current student's dissertation work. An existing name= and citations to papers using this specific type of duoidal category woul= d be much appreciated. I can't do much better than ``monoidal category with finite products''. Any such becomes duoidal in this way. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]