From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6099 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: String diagrams, adjunction and autonomous categories. Date: Fri, 3 Sep 2010 15:07:51 +0800 Message-ID: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1283556657 32123 80.91.229.12 (3 Sep 2010 23:30:57 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 3 Sep 2010 23:30:57 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sat Sep 04 01:30:54 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 1Orfig-0006w1-LS for gsmc-categories@m.gmane.org; Sat, 04 Sep 2010 01:30:54 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:47315) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OrfhZ-0001hn-7M; Fri, 03 Sep 2010 20:29:45 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OrfhV-0007ke-BR for categories-list@mlist.mta.ca; Fri, 03 Sep 2010 20:29:41 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6099 Archived-At: Mike Shulman wrote: On the other hand, am I right that you (John) have also written about > string diagrams in closed (non-autonomous) monoidal categories? Right. > Those are a bit subtler, and I don't recall them in the work of Joyal and > Street (am I wrong?). I think you're right - they're subtler, and I haven't seen anyone else using them. I never proved any *theorems* about them. But I used them extensively in my course on "Classical versus quantum computation", starting here: http://math.ucr.edu/home/baez/qg-fall2006/index.html#computation I wanted to explain how beta-reduction in the lambda calculus is like "straightening a zig-zag". There's a quick summary of this material in that "Rosetta Stone" paper with Mike Stay, mentioned earlier: http://arxiv.org/abs/0903.0340 > 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. > Oh, okay. Yeah, I was sort of disappointed that Micah credited me for string diagrams in the autonomous case, where I didn't invent them, instead of the closed case, where maybe I did. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]