From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8561 Path: news.gmane.org!not-for-mail From: David Yetter Newsgroups: gmane.science.mathematics.categories Subject: A coherence theorem question Date: Tue, 17 Mar 2015 14:25:03 +0000 Message-ID: Reply-To: David Yetter NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1426610822 7954 80.91.229.3 (17 Mar 2015 16:47:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 17 Mar 2015 16:47:02 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Tue Mar 17 17:46:54 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YXudo-0005Bu-7d for gsmc-categories@m.gmane.org; Tue, 17 Mar 2015 17:46:52 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42601) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YXud6-0000aM-Nh; Tue, 17 Mar 2015 13:46:08 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YXud2-0006Ff-RB for categories-list@mlist.mta.ca; Tue, 17 Mar 2015 13:46:04 -0300 Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8561 Archived-At: =0A= A question, that if it has a known answer would probably have been settled = long before electronically searchable media arose, came up in the project a= =A0 student of mine is working on for his dissertation.=0A= =0A= Obviously the coherence theorem for symmetric monoidal categories applies t= o cartesian monoidal categories.=A0 The question is:=A0 Is there anything b= etter?=0A= =0A= More specifically is anyone aware of (with a citation to where it is proved= ) a coherence theorem asserting a large class of diagrams commute in any ca= rtesian monoidal category, or giving criteria for their commuting, when the= =A0 diagrams are made not just prolongations of the monoidal structure maps= , but also involve projections (or equivalently unique arrows to the termin= al object 3D monoidal identity) or diagonals.=A0 (If the "or" turns out to = be exclusive, I'd be happiest for a theorem including diagonals, but not pr= ojections, since those come up more in my student's work.)=0A= =0A= Of course I'd be happy with a modern-style coherence result, characterizing= free cartesian monoidal categories, too, since we should be able to read o= ff the "all-[these] diagrams commute" sort of theorem from it.=0A= =0A= =0A= Best Thoughts,=0A= =0A= David Yetter=0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]