From: Jean-Pierre Marquis <jean-pierre.marquis@umontreal.ca>
To: "categories@mq.edu.au" <categories@mq.edu.au>
Cc: Wesley Phoa <doctorwes@gmail.com>,
"Michael Barr, Prof." <barr.michael@mcgill.ca>,
Evgeny Kuznetsov <jenkakuznecov@gmail.com>
Subject: Re: Modification of what I said
Date: Mon, 18 Dec 2023 20:08:14 +0000 [thread overview]
Message-ID: <YQXPR01MB367173F332425850714561AFDB90A@YQXPR01MB3671.CANPRD01.PROD.OUTLOOK.COM> (raw)
In-Reply-To: <CA+7H6goUBvkF3vAhK_8hhNLWQ0z277bNpuWs5fARc01xNJtQZg@mail.gmail.com>
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I guess it is a paper like this one that justified Eilenberg & Mac Lane’s choice of terminology. It would be interesting to trace how far the terminology goes back, who used it and where.
Jean-Pierre
De : Evgeny Kuznetsov <jenkakuznecov@gmail.com>
Date : lundi, 18 décembre 2023 à 14:43
À : Jean-Pierre Marquis <jean-pierre.marquis@umontreal.ca>
Cc : Wesley Phoa <doctorwes@gmail.com>, Michael Barr, Prof. <barr.michael@mcgill.ca>, categories@mq.edu.au <categories@mq.edu.au>
Objet : Re: Modification of what I said
Here is a copy of the paper by Hassler Whitney of 1938 titled "Tensor products of abelian groups"
On Mon, Dec 18, 2023, 23:32 Jean-Pierre Marquis <jean-pierre.marquis@umontreal.ca<mailto:jean-pierre.marquis@umontreal.ca>> wrote:
Most likely.
Whitney uses the terms ‘natural isomorphism’ and ‘natural homomorphism’ as well as the terms ‘natural topology’ and ‘natural neighborhood’ at many different places in the paper. But these terms are never explicitly defined.
Cheers,
Jean-Pierre
De : Wesley Phoa <doctorwes@gmail.com<mailto:doctorwes@gmail.com>>
Date : lundi, 18 décembre 2023 à 14:18
À : Michael Barr, Prof. <barr.michael@mcgill.ca<mailto:barr.michael@mcgill.ca>>
Cc : categories@mq.edu.au<mailto:categories@mq.edu.au> <categories@mq.edu.au<mailto:categories@mq.edu.au>>
Objet : Re: Modification of what I said
Was he referring to the paper “Tensor products of abelian groups”, cited in this discussion? https://mathoverflow.net/questions/287869/history-of-natural-transformations<https://protect-au.mimecast.com/s/0B0XCq71jxfo3jqzIZi0yt?domain=mathoverflow.net>
I don’t have access to it either, but it’s on Scribd: https://www.scribd.com/document/172981416/Hassler-Whitney-Tensor-Products-of-Abelian-Groups<https://protect-au.mimecast.com/s/F9RLCr810kCGYlg1czM15w?domain=scribd.com>
The terms “natural isomorphism” and “natural homomorphism” are used on pages 500-501, and these do turn out to be natural transformations, but it’s not obvious that he intended to explicitly define a new formal concept.
Wesley
Sent from my iPad
On Dec 18, 2023, at 10:00 AM, Michael Barr, Prof. <barr.michael@mcgill.ca<mailto:barr.michael@mcgill.ca>> wrote:
Peter Freyd claims that Hassler Whitney defined natural transformation in a 1938 paper. I no longer have access to Math. Reviews (except by going to McGill, which I have done only once in the last four years) so I cannot supply a reference.
Michael
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next prev parent reply other threads:[~2023-12-18 23:16 UTC|newest]
Thread overview: 10+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-12-18 17:56 Michael Barr, Prof.
2023-12-18 19:14 ` Wesley Phoa
2023-12-18 19:29 ` Jean-Pierre Marquis
2023-12-18 19:43 ` Evgeny Kuznetsov
2023-12-18 20:08 ` Jean-Pierre Marquis [this message]
2023-12-19 5:07 ` Patrik Eklund
2023-12-19 5:44 ` Dusko Pavlovic
2023-12-20 0:10 ` David Roberts
2023-12-20 21:02 ` Dusko Pavlovic
2023-12-21 3:08 ` Ross Street
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