From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8529 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: Category without objects Date: Thu, 05 Mar 2015 16:14:37 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: plane.gmane.org Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1425647768 1085 80.91.229.3 (6 Mar 2015 13:16:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 6 Mar 2015 13:16:08 +0000 (UTC) Cc: categories@mta.ca To: Jiri Adamek , Uwe Egbert Wolter Original-X-From: majordomo@mlist.mta.ca Fri Mar 06 14:16:01 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 1YTs6h-0001gj-1L for gsmc-categories@m.gmane.org; Fri, 06 Mar 2015 14:15:59 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:55159) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YTs5t-0007BL-Jp; Fri, 06 Mar 2015 09:15:09 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YTs5r-0005F0-EK for categories-list@mlist.mta.ca; Fri, 06 Mar 2015 09:15:07 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8529 Archived-At: Much older, 69-70 years old ! In the original paper: S. Eilenberg y S. Mac Lane, General Theory of Natural Equivalences, Trans. Amer. Math. Soc. 58 (1945), 231?294. They already considered the notion of category without objects, but choose to use objects. They wrote: "It is thus clear that the objects play a secondary role, and could be entirely omitted from the definition of a category. However, the manipulation of the applications would be slightly less convenient were this done. [p?g. 238] On spite of this, Ehresmann was a fan of categories without objects: Erhesman adopted and pushed forward the notion of categories without objects, writing many papers and a book where categories did not have objects. C. Ehresmann, Cat?gories topologiques et cat?gories diff?rentiables, Colloque G?om. Diff. Globale (Bruxelles, 1958), Centre Belgue Rech. Math., Louvain, 1959, 137?150. Eduardo Dubuc On 05/03/15 13:49, Jiri Adamek wrote: > See Definition 3.8 in Herrlich & Strecker: Category > Theory (42 years old...). > > Cheers > Jiri > > xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx > alternative e-mail address (in case reply key does not work): > J.Adamek@tu-bs.de > xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx > > On Thu, 5 Mar 2015, Uwe Egbert Wolter wrote: > >> Some years ago (around 30?) I read a book where it was mentioned that >> one could define categories without (explicit) objects in the sense that >> objects are mimicked by identity morphisms. Unfortunately, I can not >> reconstruct what book it was. >> >> I know how this works. I would, however, like to have a reference. >> >> Best >> >> Uwe Wolter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]