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

[David Roberts <droberts.65537@gmail.com>]

Dear Peter,

>For Saunders, the terminology of category theory came from Kant.

this is not what I mean. That 'category' came from Kant is well-known.
But when was the field itself called 'category theory'? That is, when
was it sufficiently established to warrant its own name, rather than
just be a method in algebraic topology/abstract algebra? Some early
books were titled 'Categories and functors' (albeit in German), rather
than 'Category theory', though we got there in the end!

Certainly by the publication of

Proceedings Sydney Category Theory Seminar 1972 /1973 (Springer LNM 420)

we have 'Category theory' in print (in a title in English), though
Ross pointed out Max Kelly's honours-level course "category theory" in
Sydney in 1965 (in principle one could track down the university
archives...). But 'category theory' as a phrase appears nowhere in the
1945 paper.

This was all just idle curiosity, though, so I'm happy to receive
replies off-list if the moderator deems this all too frivolous.

Best regards,
David

David Roberts
Webpage: https://ncatlab.org/nlab/show/David+Roberts
Blog: https://thehighergeometer.wordpress.com

On Thu, 11 Jul 2019 at 22:28, Peter May <may@math.uchicago.edu> wrote:
>
> 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
>
>

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