From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9949 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: Johannes Huebschmann Newsgroups: gmane.science.mathematics.categories Subject: Re: "First" use of 'Category theory' to describe our field Date: Sat, 13 Jul 2019 11:45:47 +0200 (CEST) Message-ID: References: Reply-To: Johannes Huebschmann Mime-Version: 1.0 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="127806"; mail-complaints-to="usenet@blaine.gmane.org" Cc: Peter May , "categories@mta.ca list" , To: David Roberts Original-X-From: majordomo@mlist.mta.ca Sat Jul 13 21:07:54 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1hmNNC-000X3y-JJ for gsmc-categories@m.gmane.org; Sat, 13 Jul 2019 21:07:54 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:34769) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1hmNMt-0005OP-46; Sat, 13 Jul 2019 16:07:35 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1hmNM6-0000ux-GM for categories-list@mlist.mta.ca; Sat, 13 Jul 2019 16:06:46 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9949 Archived-At: 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" =C3=80: "Peter May" Cc: "categories@mta.ca list" Envoy=C3=A9: Jeudi 11 Juillet 2019 15:12:10 Objet: categories: Re: "First" use of 'Category theory' to describe our fie= ld 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 wrote: > > For Saunders, the terminology of category theory came from Kant. From Wi= kipedia: > > In Kant's philosophy, a category (German: Categorie in the original or Ka= tegorie 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/ ]