"First" use of 'Category theory' to describe our field
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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<mailto: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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
There's a nice Wikipedia article on "General Abstract Nonsense", but not on the more formal name. On Fri, Jul 12, 2019, 3:45 PM 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 <mailto: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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
From memory, the Pure Mathematics Honours (USyd) course that Max Kelly taught in 1965 was called ``Category Theory''.
While I don't recall the course title, my recollection is that the year Max taught category theory to Ross and other third year students was 1964. Max was going to move on to algebraic topology in 1965 (our honours year, 14 in that class including Brian Day and Henry Irgang) until he realized we'd never seen point set topology so he settled for that. The first homework for the latter was to enumerate the T0 spaces up to three points (or perhaps four, which is still feasible for a homework though tedious). In those days I was much more at home with combinatorics than algebra so that was a fun homework for me. Maybe that's why I ended up in computer science. I didn't really warm to algebra until 1979, in particular universal algebra courtesy of Rasiowa and Sikorski, despite having taught a groups-rings-fields course at MIT in 1972, and it was a couple of years more before I started to come to grips with categories. Vaughan On Sat, Jul 13, 2019 at 12:06 PM La Monte H. P. Yarroll < piggy.yarroll@gmail.com> wrote:
There's a nice Wikipedia article on "General Abstract Nonsense", but not on the more formal name.
On Fri, Jul 12, 2019, 3:45 PM 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 <mailto: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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
In the preface of Eilenberg-Mac Lane: Collected works, EML write (on p.ix/x): Category theory was thus born very quietly in 1945. ... It was only with Grothendieck's famous Tohoku paper in 1957 that the theory came into full bloom. Grothendieck already exploited, among other things, abelian categories. The term category derives form the ancient Greek verb kategoreo. Johannes ----- Mail original ----- De: "David Roberts" <droberts.65537@gmail.com> À: "categories@mta.ca list" <categories@mta.ca> Envoyé: Mercredi 10 Juillet 2019 14:01:16 Objet: categories: "First" use of 'Category theory' to describe our field 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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
For Saunders, the terminology of category theory came from Kant.?? From Wikipedia: In Kant's philosophy, a category (German: Categorie in the original or Kategorie in modern German) is a *pure concept of the understanding (Verstand)*. Etc.?? It may be relevant that Saunders was very influenced by his time at Gottingen. In any case, the term category theory was second nature to him. Although that was well before my time, I'm quite sure he used the term pretty much from the beginning. On 7/10/19 7:01 AM, 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 name?
Answers referring to verifiable sources would be best.
Thoughts?
David
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I don't think anyone used the term category theory (in the mathematical sense) before mathematical biologist Robert Rosen in 1958. That is the earliest reference known to Math Reviews. Not surprising, it was slow to spread from Rosen into the field. Saunders mentioned "the theory of categories" once in his 1963 book Homology (p. 34). In that book he writes repeatedly of set theory, group theory, homology theory, and many others, but not once "category theory". One other datum: Freyd's 1960 dissertation was titled "Functor theory," but "category theory" occurs in the introduction to the 1964 book version. Category theory was a very common term by the late 1960s. Good question about "category theorist." I have no idea but expect it came several years later. It is not used very formally, and searching it on Math Reviews gives only 15 hits in the entire database. Colin On 7/10/19 7:01 AM, 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 name?
Answers referring to verifiable sources would be best.
Thoughts?
David
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (7)
-
Colin McLarty -
David Roberts -
Johannes Huebschmann -
La Monte H. P. Yarroll -
Peter May -
Ross Street -
Vaughan Pratt