From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8532 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Category without objects Date: Sat, 07 Mar 2015 14:36:36 +0000 Message-ID: References: Reply-To: Ronnie Brown NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1425779107 5132 80.91.229.3 (8 Mar 2015 01:45:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 8 Mar 2015 01:45:07 +0000 (UTC) Cc: Categories list To: Uwe Egbert Wolter , Peter LeFanu Lumsdaine Original-X-From: majordomo@mlist.mta.ca Sun Mar 08 02:44:59 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.127]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1YUQH4-00081O-Nk for gsmc-categories@m.gmane.org; Sun, 08 Mar 2015 02:44:58 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57679) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YUQG2-00031U-14; Sat, 07 Mar 2015 21:43:54 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YUQG2-0005zc-A2 for categories-list@mlist.mta.ca; Sat, 07 Mar 2015 21:43:54 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8532 Archived-At: I remember Henry Whitehead said that he was very impressed by the axioms for a category in the Eilenberg-Mac Lane paper. A curiosity about the definition is that groupoids were defined by Brandy in 1926, and this definition was used by the Chicago school of algebra and applied to ring theory. Bill Cockcroft told me that the groupoid notion was an influence. In 1985 I asked Eilenberg about this, and said no, since if it had been, they would have used it as an example! I forgot to ask Mac Lane! Ronnie Brown On 06/03/2015 14:42, Uwe Egbert Wolter wrote: > Many thanks for all the immediate replies and all the interesting > information. > > Finally, I could also reconstruct today where I have seen the > arrows-only definition around 30 years ago. There is a four page > introduction into categories in the first chapter of P.M. Cohn's > "Universal Algebra". He outlines that one could do so and gives a > corresponding exercise. > > Best > > Uwe > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]