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, but 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 Dave was Peter Freyd's undergraduate advisor at Brown where Peter really discovered his abelian categories embedding theorem.

Dave also predicted that by the turn of century, categories 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 from the latter to the former until I spent 6 months in Zurich in 1967 at the Mathematische Forschunginstitut (which we sometimes called the Eckmann-Hilton).

Michael
From: David Roberts <droberts.65537@gmail.com>
Sent: Thursday, February 22, 2024 9:24 PM
To: categories@mq.edu.au <categories@mq.edu.au>; Ross Street <ross.street@mq.edu.au>
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 that Freyd's 1960 PhD thesis was titled "Functor theory", at Princeton, supervised by Steenrod and Buchsbaum. I suspect it was largely influenced 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 conjecture that the name "category theory" really didn't emerge quite yet at that time, 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 <droberts.65537@gmail.com>
Date: Sat, 13 Jul 2019 at 05:13
Subject: categories: Re: "First" use of 'Category theory' to describe 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.
> Also John Gray's (UIllinois) 1968-69 graduate course had that name.
>
> From Eilenberg I heard that each person using categories should have their 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 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 <droberts.65537@gmail.com> 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 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
>


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