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boundary="000000000000017380060ccdf606" --000000000000017380060ccdf606 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Here is a copy of the paper by Hassler Whitney of 1938 titled "Tensor produ= cts of abelian groups" On Mon, Dec 18, 2023, 23:32 Jean-Pierre Marquis > wrote: Most likely. Whitney uses the terms =E2=80=98natural isomorphism=E2=80=99 and =E2=80=98n= atural homomorphism=E2=80=99 as well as the terms =E2=80=98natural topology= =E2=80=99 and =E2=80=98natural neighborhood=E2=80=99 at many different plac= es in the paper. But these terms are never explicitly defined. Cheers, Jean-Pierre De : Wesley Phoa > Date : lundi, 18 d=C3=A9cembre 2023 =C3=A0 14:18 =C3=80 : Michael Barr, Prof. > Cc : categories@mq.edu.au > Objet : Re: Modification of what I said Was he referring to the paper =E2=80=9CTensor products of abelian groups=E2= =80=9D, cited in this discussion? https://mathoverflow.net/questions/287869= /history-of-natural-transformations I don=E2=80=99t have access to it either, but it=E2=80=99s on Scribd: https= ://www.scribd.com/document/172981416/Hassler-Whitney-Tensor-Products-of-Abe= lian-Groups The terms =E2=80=9Cnatural isomorphism=E2=80=9D and =E2=80=9Cnatural homomo= rphism=E2=80=9D are used on pages 500-501, and these do turn out to be natu= ral transformations, but it=E2=80=99s not obvious that he intended to expli= citly define a new formal concept. Wesley Sent from my iPad On Dec 18, 2023, at 10:00=E2=80=AFAM, Michael Barr, Prof. > wrote: =EF=BB=BF 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 sup= ply a reference. Michael You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | Learn = more about Microsoft 365 Groups You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --000000000000017380060ccdf606 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Here is a copy of the paper by Hassler Whitney of 19= 38 titled "Tensor products of abelian groups"



On Mon, Dec 18, 2023, 23:32 Jean-Pier= re Marquis <jean-pierre.marquis@umontreal.ca> wrote:

Most likely.<= /p>

 

Whitney uses the terms =E2=80= =98natural isomorphism=E2=80=99 and =E2=80=98natural homomorphism=E2=80=99 = as well as the terms =E2=80=98natural topology=E2=80=99 and =E2=80=98natura= l neighborhood=E2=80=99 at many different places in the paper. But these te= rms are never explicitly defined.

 

Cheers,

 

Jean-Pierre

 

 

De = ;: Wesley Phoa <doctorwes@gmai= l.com>
Date : lundi, 18 d=C3=A9cembre 2023 =C3=A0 14:18
=C3=80 : 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 =E2=80=9CTensor produc= ts of abelian groups=E2=80=9D, cited in this discussion? https://m= athoverflow.net/questions/287869/history-of-natural-transformations<= /u>

 

I don=E2=80=99t have access to it either, but it=E2= =80=99s on Scribd: https://www.scribd.com/document/172981416/Hassler-Whi= tney-Tensor-Products-of-Abelian-Groups

 

The terms =E2=80=9Cnatural isomorphism=E2=80=9D and = =E2=80=9Cnatural homomorphism=E2=80=9D are used on pages 500-501, and these= do turn out to be natural transformations, but it=E2=80=99s not obvious th= at he intended to explicitly define a new formal concept.

 

Wesley

 

Sent from my iPad



On Dec 18, 2023, at 1= 0:00=E2=80=AFAM, Michael Barr, Prof. <barr.mic= hael@mcgill.ca> wrote:

=EF=BB=BF

Peter Freyd claims that Hassler Whitney d= efined natural transformation in a 1938 paper.  I no longer have acces= s to Math. Reviews (except by going to McGill, which I have done only once in the last four years) so I cannot supply a referen= ce.

 

Michael

 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files =   |   = Lea= ve group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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