From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9331 Path: news.gmane.org!.POSTED!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Fred Date: Wed, 6 Sep 2017 23:07:01 -0700 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1504795988 25851 195.159.176.226 (7 Sep 2017 14:53:08 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 7 Sep 2017 14:53:08 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Thu Sep 07 16:52:51 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dpy9Z-0003c4-CY for gsmc-categories@m.gmane.org; Thu, 07 Sep 2017 16:51:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:37389) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dpyAo-0004OV-43; Thu, 07 Sep 2017 11:52:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dpy97-00083D-KX for categories-list@mlist.mta.ca; Thu, 07 Sep 2017 11:51:09 -0300 In-Reply-To: Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9331 Archived-At: Even though I was one of the dozen students, along with Ross Street and Brian Day, who took Max Kelly's course in category theory at the University of Sydney in 1965, unlike them I went in other directions thereafter.?? It is therefore a bit surprising that I kept bumping into Fred Linton, who turned out to have other interests that kept bringing me into contact with him over the past four decades in matters arguably unrelated to category theory: computer software, Jonsson-Tarski algebras, electrical engineering, 3D rendering of knots, etc. But it is Fred's foundational work on monads that I want to comment on here.???? At UACT, the Universal Algebra and Category Theory meeting at MSRI organized by respectively Ralph McKenzie and Saunders Mac Lane in 1992, there were back-to-back talks in a late-morning two-talk session on what I like to think of today as the foundations of equational model theory, EML.?? These were given by Walt Taylor and Fred Linton in that order. Ok, so who here noticed these two talks were both on EML??? Not me, I was a computer scientist still getting acclimated to such abstractions.?? Maybe some people, but if so the connection passed entirely without comment at the time, like ships passing in the night, and we all headed off for lunch. At lunch I sat with George McNulty, Walt's coauthor along with Ralph McKenzie of the classic UA text /Algebras, lattices, varieties/, Volume 1, 1987, the book that took two pages to explain why (for any given signature with no constants) the empty algebra was a bad idea. As a result of my much earlier work on dynamic algebras George and I went back several years and he was keen to understand what Fred had been on about in his just-ended talk.?? So with the fervor of a missionary I launched into monad theory, which I'd been teaching at Stanford for several years. No luck.?? In retrospect what I should have done instead was try to make some sort of connection between Walt's and Fred's two back-to-back talks on EML. In my mind, whether fairly or unfairly, what distinguished Fred from his fellow category theorists at UACT was that he was the natural CT representative of EML. There is one other anecdote about UACT, nothing to do with Fred, that I have always loved.?? In the course of MSRI director Bill Thurston's opening remarks, he said words to the effect that the notion of the opposite of a category made him nauseous.?? This was the only meeting I have ever attended where fully half the attendees drew in enough breath to drop the air pressure by an audible amount. ??Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]