Re: "First" use of 'Category theory' to describe our field

[Vaughan Pratt <pratt@cs.stanford.edu>]

  > 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
>>

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