From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: * X-Spam-Status: No, score=1.8 required=5.0 tests=DATE_IN_PAST_06_12, LOCALPART_IN_SUBJECT,RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 12326 invoked from network); 30 Jan 2023 20:12:38 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 30 Jan 2023 20:12:38 -0000 Received: from rr.mta.ca ([198.164.44.159]:40440) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pMaVz-00010V-QG; Mon, 30 Jan 2023 16:12:31 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pMaV4-0005zX-5Z for categories-list@rr.mta.ca; Mon, 30 Jan 2023 16:11:34 -0400 Date: Mon, 30 Jan 2023 10:43:47 +0100 From: =?ISO-8859-15?Q?Jir=ED_Ad=E1mek?= To: categories net Subject: categories: Bill Lawvere MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII"; format=flowed Precedence: bulk Reply-To: =?ISO-8859-15?Q?Jir=ED_Ad=E1mek?= Message-Id: I am very sad that Bill Lawevere, a great mathematician and a great man, has passed away. Jiri Rosicky and I had the extraordinary good luck of working on several joint articles with Bill, and we have very happy memories of that collaboration. It started after the publication of our book on locally presentable categories in 1994: Bill approached us shortly after that with the suggestion to study what properties make locally presentable 'tick'. We had difficuties understanding his suggestion, and during the discussions about that we have realized that nobody had studied the algebraic duality that would be the analogy of the Gabriel-Umer duality to finitary varieties. This led to our first short joint paper. Later Bill came with the suggestion to have a look at 'how algebraic is algebra': is there a higher-order monad whose algebras are finitary varieties? In one of his early mails on that topic he wrote that the answer would probably depend on Ulam cardinals. (A concept we two had not heard of before.) We spent months of intensive work on this topic during which Bill's impulses were the much needed support in times when there seemed to be no light at the end of the tunnel. But eventually light came, and we published two joint papers, about varieties and about locally finitely presentable categories. One of our basic results needed the assumption of non-existence of measurable cardinals. Only then did we two learned that they are also called Ulam cardinals- our admiration for Bill's insight could not have been greater... One day Bill came with the grand idea of a initiating a collection of monographs on topics he found important. At first a group of enthusiastic colleagues agreed to start working on the project, but as time went on, one after another decided to quit. In the end, just one monograph was realized, the joint book with Jiri Rosicky and Enrico Vitale on algebraic theories. Bill followed our work on it closely, supporting us and criticizing what he did not find right. We were proud when he agreed to write a preface to it. During all the time of our collaboration with Bill he was extremely patient and friendly. It is indeed a very sad news that this great and kind man has passed away. Jiri Adamek [For admin and other information see: http://www.mta.ca/~cat-dist/ ]