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

[Johannes Huebschmann <johannes.huebschmann@univ-lille.fr>]

Dear All

The phrase

"the terminology of category theory came from Kant"

oversimplifies the situation.

Aristotle (Peri ton kategorion)
discusses categories.
Kant uses categories to mediate his thought
(Kritik der Urteilskraft).
Saunders Mac Lane's adviser in Goettingen was
Paul Bernays. Bernays knew ancient Greek philosophy
very well.

During my student's time
at the ETH I still had occasion to talk
to Paul Bernays (he then was in his 80s).
He regularly attended the
logic seminar and even contributed to the discussion.

As for the terminology "functor" I vaguely remember
this derives from Carnap but I may be wrong
and perhaps my memory fails.
Perhaps someone knows better.

Also, in German, when you teach a course entitled "Kategorien"
or "Kategorien und Funktoren",
that synonymously means "Kategorientheorie".
For example, D. Puppe taught such a course in the 1960s,
and that was the origin of the Brinkmann-Puppe LNM.


Best regards

Johannes


----- Mail original -----
De: "David Roberts" <droberts.65537@gmail.com>
À: "Peter May" <may@math.uchicago.edu>
Cc: "categories@mta.ca list" <categories@mta.ca>
Envoyé: Jeudi 11 Juillet 2019 15:12:10
Objet: categories: Re: "First" use of 'Category theory' to describe our field

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.
>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]