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=1.5 required=5.0 tests=DATE_IN_PAST_12_24, LOCALPART_IN_SUBJECT,RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 16848 invoked from network); 2 Feb 2023 21:42:14 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 2 Feb 2023 21:42:14 -0000 Received: from rr.mta.ca ([198.164.44.159]:41146) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pNhKT-0000JU-5f; Thu, 02 Feb 2023 17:41:13 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pNhK6-0002KY-3t for categories-list@rr.mta.ca; Thu, 02 Feb 2023 17:40:50 -0400 From: Ross Street To: categories@mta.ca Subject: categories: Bill Lawvere Date: Thu, 2 Feb 2023 09:12:36 +0000 Accept-Language: en-GB, en-US Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Precedence: bulk Reply-To: Ross Street Message-Id: =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Yesterday our Seminar started again after our summer break. Local people ar= e attending in person although zoom is still used. I arrived early since th= ere were some things I wanted to find in my office: non-computer-file mater= ial. I moved rooms recently so some papers are in mysterious places. Not so= my remaining books. These are all in nice alphabetical order according to = author. Recently I started talking mathematics with a last-year-of-high-school stud= ent and so far it is ongoing. I wanted to consult my copy of the book ``Co= nceptual Mathematics'' to see how some things were treated there. The autho= rs Bill Lawvere and Steve Schanuel inscribed my copy on the inside cover. T= hose words, confirming what people have been writing about Bill, spurred me= to write these personal memories. Bill wrote: ``For Ross Street, In appreciation of the many inspiring mathem= atical discussions in Sydney and around the World, and in recognition of co= -participation in the great struggle for improved teaching of science. And = with warm affection, Bill Lawvere.'' (After that came: ``Me too, Steve Scha= nuel.'') As a PhD student at the University of Sydney, the papers in the LaJolla 196= 5 Conference on Categorical Algebra had a big influence on me. In particula= r, I found the one by Bill (first in the volume) quite remarkable. I had st= arted worrying about foundations of mathematics a few years earlier. Bill's= ideas were not what I had read in Russell! I first met Bill in 1968-69 while I was a postdoc at the University of Illi= nois, 120 miles south of Chicago. In mid-1969 (when a USA citizen was takin= g one small step), we met for longer at the Summer School on Category Theor= y, Bowdoin College, Maine. The lecture of Bill that I remember was about me= tric spaces as enriched categories. Anyone familiar with my publications an= d those of my colleague Bob Walters will know what an influence that work h= ad on us. I think it was at Oberwolfach in 1972 when I nervously gave my talk on Yone= da structures that Bill suggested maybe my 2-category should have a tensor = product. Around that time, Brian Day took some notes of Bill's lectures in = Aarhus on quite a few topics including monoidal bicategories. Soon after we saw John Gray's summary of talks in a conference at the ETH, = Z\"urich. The talk by Myles Tierney announced one huge step for mathematics= : the concept of Elementary Topos. This was joint work with Bill, of course= . The application connecting forcing to sheaf theory was absolutely brillia= nt. However, it is the simplicity of the topos axioms that is truly beautif= ul. With further suggestions from Bill and input from Anders Kock, Chris Mi= kkelsen and Bob Par\'e, the axioms reduced even further. The elementary top= os fan club just grows and grows (to elephant proportions). I was greatly h= onoured to hear that Bill was giving my Survey of Topos Theory notes to his= graduate students to read. When Bill visited the University of Sydney, Steve Schanuel visited Macquari= e. These were wonderful times for our mathematics. Both men reached out bey= ond the category theorists, inspiring the two departments. Other people ove= rlapped with these visits: for example, Dold, Heller at Macquarie (with Sch= anuel keen on trace, Euler characteristic and homotopy theories) and Carbon= i (with Lawvere keen on enrichment in monoidal bicategories) at Sydney. I was invited to SUNY Buffalo several times. With Duskin, Isbell, Lawvere, = Schanuel, Schack, and others, there was plenty to discuss in the Department= common room (``Steve's office''). I was honoured to deliver the John Myhil= l Memorial Lectures for 1993. Bill showed great enthusiasm for the topics. As category theory is embraced by the wider community, Bill's contributions= will live on and be admired. =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D [For admin and other information see: http://www.mta.ca/~cat-dist/ ]