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

[Ross Street <ross.street@mq.edu.au>]

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
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