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charset="Windows-1252" Content-Transfer-Encoding: quoted-printable I just heard from Peter Freyd who tells me that some of things in my earlie= r message were wrong. The person at Brown who most influenced him was Davi= d Buchsbaum who later became one of his thesis acvisors at Princeton (Steen= rod was the other). And in fact, Peter told me that Dave Harrison may have= first heard of categories from him. Buchsbaum (a student of Eilenberg's) = wrote a paper called something like Exact categories, giving essentially th= e definition of abelian categories. The latter name is probably due to Gro= thendieck in his famous Tohoku paper. Later on, not knowing that term had = been used already, I used exact categories for a non-additive version. At = least exact+additive is equivalent to abelian. Peter is not using email these days so if you want his story you have to ta= lk (or zoom) with him. BTW, an English translation of Grothendieck's paper= prepared by my wife with some help from me is available on my web site. Michael ________________________________ From: Michael Barr, Prof. Sent: Friday, February 23, 2024 12:07 PM To: David Roberts ; categories@mq.edu.au ; Ross Street Subject: Re: categories: Re: "First" use of 'Category theory' to describe o= ur field I don't know when I first heard the term "category theory". Interestingly,= the 1965 conference in La Jolla called itself a conference on categorical = algebra. The n-lab page says it was "on categorical algebra, nominally, bu= t really about fundamental category theory as such, to a large extent." I know when I first heard the word category in this context. In 1959-60 I = took a course on homological algebra from Dave Harrison (my eventual thesis= advisor) and he talked about categories at length. I might mention that D= ave was Peter Freyd's undergraduate advisor at Brown where Peter really dis= covered his abelian categories embedding theorem. Dave also predicted that by the turn of century, categories would have repl= aced sets as the foundation of mathematics. We are not there yet. In thos= e days, category theory and homological algebra were closely entwined. I d= idn't turn from the latter to the former until I spent 6 months in Zurich i= n 1967 at the Mathematische Forschunginstitut (which we sometimes called th= e Eckmann-Hilton). Michael ________________________________ From: David Roberts Sent: Thursday, February 22, 2024 9:24 PM To: categories@mq.edu.au ; Ross Street Subject: Fwd: categories: Re: "First" use of 'Category theory' to describe = our field Hi all, It's been a few years, but it came to my attention in the past 24 hours tha= t Freyd's 1960 PhD thesis was titled "Functor theory", at Princeton, superv= ised by Steenrod and Buchsbaum. I suspect it was largely influenced by Buch= sbaum, being a student of Eilenberg, and who essentially introduced abelian= categories, with which Freyd's PhD was largely about; more precisely, embe= dding theorems and hence a study of suitable functor categories. It's not a strong data point, but I think it lends weight to the conjecture= that the name "category theory" really didn't emerge quite yet at that tim= e, at least in print. All the best, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com ---------- Forwarded message --------- From: David Roberts > Date: Sat, 13 Jul 2019 at 05:13 Subject: categories: Re: "First" use of 'Category theory' to describe our f= ield To: Ross Street > Cc: categories@mta.ca list > Dear Ross, no, that's pretty good! It's mildly surprising that it took ~20 years for the name to 'stick', but maybe less so given that the field grew slowly to start. Thanks, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com On Thu, 11 Jul 2019 at 08:21, Ross Street > wrote: > > Dear David > > From memory, the Pure Mathematics Honours (USyd) course that Max Kelly ta= ught in 1965 > was called ``Category Theory''. It concentrated on different kinds of mor= phisms > and factorizations in a category, and finished with adjoint functors. > Also John Gray's (UIllinois) 1968-69 graduate course had that name. > > From Eilenberg I heard that each person using categories should have thei= r own category of expertise. > I told this to John Gray who said that was fine; the time had come for th= at category to be Cat. > > I would suggest that the first category theorists to think of themselves = as such were Eilenberg's students at Columbia. > However, Mac Lane was definitely a category theorist. > > This is probably not the verifiable stuff you were seeking. > > Ross > > > On 10 Jul 2019, at 10:01 PM, David Roberts > wrote: > > Hi all, > > the (idle) question is: when did the phrase 'category theory' catch on > for the field? Clearly it didn't leap from either of the heads of > Eilenberg or Mac Lane full-grown, since they used the phrase 'General > theory of natural equivalences'. There are the old 'Reports of the > Midwest Category Seminar' lecture notes (the first in 1967), which > hints that 'category theory' wasn't quite the name in use. > > Even more interesting: who was the first "category theorist", by that nam= e? > > Answers referring to verifiable sources would be best. > > Thoughts? > > David > > > > David Roberts > Webpage: https://ncatlab.org/nlab/show/David+Roberts > Blog: https://thehighergeometer.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] 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 --_000_YQXPR01MB3927A537918FA02F2DD508BE9C552YQXPR01MB3927CANP_ Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable
I just heard from Peter Freyd who tells me that some of things in my earlie= r message were wrong.  The person at Brown who most influenced him was= David Buchsbaum who later became one of his thesis acvisors at Princeton (= Steenrod was the other).  And in fact, Peter told me that Dave Harrison may have first heard of categories from h= im.  Buchsbaum (a student of Eilenberg's) wrote a paper called somethi= ng like Exact categories, giving essentially the definition of abelian cate= gories.  The latter name is probably due to Grothendieck in his famous Tohoku paper.  Later on, not knowin= g that term had been used already, I used exact categories for a non-additi= ve version.  At least exact+additive is equivalent to abelian. 

Peter is not using email these days so if you want his story you have to ta= lk (or zoom) with him.  BTW, an English translation of Grothendieck's = paper prepared by my wife with some help from me is available on my web sit= e.

Michael
From: Michael Barr, Prof. &= lt;barr.michael@mcgill.ca>
Sent: Friday, February 23, 2024 12:07 PM
To: David Roberts <droberts.65537@gmail.com>; categories@mq.ed= u.au <categories@mq.edu.au>; Ross Street <ross.street@mq.edu.au>= ;
Subject: Re: categories: Re: "First" use of 'Category theo= ry' to describe our field
 
I don't know when I first heard the term "category t= heory".  Interestingly, the 1965 conference in La Jolla called itself a conference on categorical algebra.  The n= -lab page says it was "on categorical algebra, nominally, but really a= bout fundamental category theory as such, to a large extent."

I know when I first heard the word category in this conte= xt.  In 1959-60 I took a course on homological algebra from Dave Harrison (my eventual thesis advisor) and he talked abou= t categories at length.  I might mention that Dave was Peter Freyd's u= ndergraduate advisor at Brown where Peter really discovered his abelian cat= egories embedding theorem.

Dave also predicted that by the turn of century, categori= es would have replaced sets as the foundation of mathematics.  We are not there yet.  In those days, category = theory and homological algebra were closely entwined.  I didn't turn f= rom the latter to the former until I spent 6 months in Zurich in 1967 at th= e Mathematische Forschunginstitut (which we sometimes called the Eckmann-Hilton).

Michael
From: David Roberts <d= roberts.65537@gmail.com>
Sent: Thursday, February 22, 2024 9:24 PM
To: categories@mq.edu.au <categories@mq.edu.au>; Ross Street &= lt;ross.street@mq.edu.au>
Subject: Fwd: categories: Re: "First" use of 'Category the= ory' to describe our field
 
Hi all,

It's been a few years, but it came to my attention in the past 24 hour= s that Freyd's 1960 PhD thesis was titled "Functor theory", at Pr= inceton, supervised by Steenrod and Buchsbaum. I suspect it was largely inf= luenced by Buchsbaum, being a student of Eilenberg, and who essentially introduced abelian categories, with which Freyd's PhD = was largely about; more precisely, embedding theorems and hence a study of = suitable functor categories.

It's not a strong data point, but I think it lends weight to the conje= cture that the name "category theory" really didn't emerge quite = yet at that time, at least in print.

All the best,
David



---------- Forwarded message ----= -----
From: David Roberts <droberts.65537@gmail.com>
Date: Sat, 13 Jul 2019 at 05:13
Subject: categories: Re: "First" use of 'Category theory' to desc= ribe our field
To: Ross Street <ross.street@mq= .edu.au>
Cc: categories@mta.ca list <categories@mta.ca>


Dear Ross,

no, that's pretty good! It's mildly surprising that it took ~20 years
for the name to 'stick', but maybe less so given that the field grew
slowly to start.

Thanks,

David

David Roberts
Webpage: https://ncatlab.org/nlab/show/David+Roberts
Blog: https://thehighergeometer.wordpress.com

On Thu, 11 Jul 2019 at 08:21, Ross Street <ross.street@mq.edu.au> wrote:
>
> Dear David
>
> From memory, the Pure Mathematics Honours (USyd) course that Max Kelly= taught in 1965
> was called ``Category Theory''. It concentrated on different kinds of = morphisms
> and factorizations in a category, and finished with adjoint functors.<= br> > Also John Gray's (UIllinois) 1968-69 graduate course had that name. >
> From Eilenberg I heard that each person using categories should have t= heir own category of expertise.
> I told this to John Gray who said that was fine; the time had come for= that category to be Cat.
>
> I would suggest that the first category theorists to think of themselv= es as such were Eilenberg's students at Columbia.
> However, Mac Lane was definitely a category theorist.
>
> This is probably not the verifiable stuff you were seeking.
>
> Ross
>
>
> On 10 Jul 2019, at 10:01 PM, David Roberts <droberts.65537@gmail.com> wro= te:
>
> Hi all,
>
> the (idle) question is: when did the phrase 'category theory' catch on=
> for the field? Clearly it didn't leap from either of the heads of
> Eilenberg or Mac Lane full-grown, since they used the phrase 'General<= br> > theory of natural equivalences'. There are the old 'Reports of the
> Midwest Category Seminar' lecture notes (the first in 1967), which
> hints that 'category theory' wasn't quite the name in use.
>
> Even more interesting: who was the first "category theorist"= , by that name?
>
> Answers referring to verifiable sources would be best.
>
> Thoughts?
>
> David
>
>
>
> David Roberts
> Webpage: https://ncatlab.org/nlab/show/David+Roberts
> Blog: https://thehighergeometer.wordpress.com
>


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
 
 
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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