From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6093 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: String diagrams, adjunction and autonomous categories. Date: Thu, 2 Sep 2010 11:23:01 -0700 Message-ID: References: Reply-To: Michael Shulman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1283556400 31289 80.91.229.12 (3 Sep 2010 23:26:40 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 3 Sep 2010 23:26:40 +0000 (UTC) Cc: categories To: John Baez Original-X-From: majordomo@mlist.mta.ca Sat Sep 04 01:26:39 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OrfeZ-0005W2-0N for gsmc-categories@m.gmane.org; Sat, 04 Sep 2010 01:26:39 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36594) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OrfdT-00016s-38; Fri, 03 Sep 2010 20:25:31 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OrfdP-0007ck-Sv for categories-list@mlist.mta.ca; Fri, 03 Sep 2010 20:25:28 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6093 Archived-At: On the other hand, am I right that you (John) have also written about string diagrams in closed (non-autonomous) monoidal categories? Those are a bit subtler, and I don't recall them in the work of Joyal and Street (am I wrong?). The original question used the word "autonomous" but the notation used suggested a merely closed monoidal category, so perhaps that's what he had in mind. Mike On Mon, Aug 30, 2010 at 10:06 PM, John Baez wrote: > Micah wrote: > > Incidentally, although I'm not sure that I'm familiar with the work of Baez >> to which you refer, I would imagine that the use of string diagrams to >> describe units and counits in an autonomous category is considerably older, >> at least as far back as "Planar Diagrams and Tensor Algebra" by Joyal and >> Street (available on the website of the latter) from 1988. >> > > He was probably talking about these popularizations: > > A prehistory of n-categorical physics, with Aaron Lauda > http://arxiv.org/abs/0908.2469 > > Physics, logic, computation and topology: a Rosetta stone, with Mike Stay > http://arxiv.org/abs/0903.0340 > > which cite the work of Joyal and Street, though sadly not the paper you > mention. > > Best, > jb > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]