Re: "First" use of 'Category theory' to describe our field
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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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<mailto: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<mailto:ross.street@mq.edu.au>> Cc: categories@mta.ca<mailto:categories@mta.ca> list <categories@mta.ca<mailto: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<mailto: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
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 mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>
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<mailto: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<mailto:ross.street@mq.edu.au>> Cc: categories@mta.ca<mailto:categories@mta.ca> list <categories@mta.ca<mailto: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<mailto: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
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 mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>
I just heard from Peter Freyd who tells me that some of things in my earlier 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 him. Buchsbaum (a student of Eilenberg's) wrote a paper called something like Exact categories, giving essentially the definition of abelian categories. The latter name is probably due to Grothendieck 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 talk (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. <barr.michael@mcgill.ca> Sent: Friday, February 23, 2024 12:07 PM To: David Roberts <droberts.65537@gmail.com>; categories@mq.edu.au <categories@mq.edu.au>; Ross Street <ross.street@mq.edu.au> Subject: Re: categories: Re: "First" use of 'Category theory' to describe our 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, 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<mailto: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<mailto:ross.street@mq.edu.au>> Cc: categories@mta.ca<mailto:categories@mta.ca> list <categories@mta.ca<mailto: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<mailto: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
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 mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>
Systems biologist Robert Rosen used the term "category theory" on p. 340 of Rosen, R. 1958. The Representation of Biological Systems from the Stand- point of the Theory of Categories. Bulletin of Mathematical Biophysics 20, 317– 342. On Thu, Feb 22, 2024 at 10:09 PM David Roberts <droberts.65537@gmail.com<mailto:droberts.65537@gmail.com>> wrote: 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<mailto: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<mailto:ross.street@mq.edu.au>> Cc: categories@mta.ca<mailto:categories@mta.ca> list <categories@mta.ca<mailto: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<mailto: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
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 mailing list group from Macquarie University. To take part in this conversation, 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 mailing list group from Macquarie University. To take part in this conversation, reply all to this message. View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>
participants (3)
-
Colin McLarty -
David Roberts -
Michael Barr, Prof.