From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5506 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: categories are beautiful Date: Sun, 10 Jan 2010 17:10:44 -0200 Message-ID: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1263168107 910 80.91.229.12 (11 Jan 2010 00:01:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 11 Jan 2010 00:01:47 +0000 (UTC) To: Categories list Original-X-From: categories@mta.ca Mon Jan 11 01:01:39 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NU7j0-0005yd-FE for gsmc-categories@m.gmane.org; Mon, 11 Jan 2010 01:01:38 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NU7Q8-0004vw-Tb for categories-list@mta.ca; Sun, 10 Jan 2010 19:42:08 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5506 Archived-At: At the beginning Ehresmann arrived to the notion of category from groupoids, even topological groupoids. These are "internal and small". They do not even have objects (just a partially defined operation with enough neutral elements). At the beginning Eilemberg-MacLane arrived to the notion of category from the categories of Sets, Groups, etc. They have objects, and are "external and large". They were not even aware that groupoids were categories. They are two very different things, that happen (by chance ?) to satisfy the same axiomatic definition of category, which is a beautiful definition. Bob Pare is so much right telling us that the distinction is not of size. Clearly the small categories of finitely presented rings, of finite groups, etc, etc, and even the groupoid of finite sets and bijective functions (in Joyal's theory of species for example) are in spirit Eilember-MacLane's "large" categories, and not Ehreshmann's "small" categories. e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]