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"

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>
Date : lundi, 18 décembre 2023 à 14:18
À : Michael Barr, Prof. <barr.michael@mcgill.ca>
Cc : categories@mq.edu.au <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

 

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

 

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> 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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