From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8528 Path: news.gmane.org!not-for-mail From: =?iso-8859-1?Q?Ren=E9_Guitart?= Newsgroups: gmane.science.mathematics.categories Subject: Re: Category without objects Date: Thu, 5 Mar 2015 19:55:42 +0100 Message-ID: References: Reply-To: =?iso-8859-1?Q?Ren=E9_Guitart?= NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1085) Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1425647692 32238 80.91.229.3 (6 Mar 2015 13:14:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 6 Mar 2015 13:14:52 +0000 (UTC) Cc: categories@mta.ca To: Uwe Egbert Wolter Original-X-From: majordomo@mlist.mta.ca Fri Mar 06 14:14:38 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 1YTs5L-0000Uw-3u for gsmc-categories@m.gmane.org; Fri, 06 Mar 2015 14:14:35 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:55149) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YTs4G-00072t-4t; Fri, 06 Mar 2015 09:13:28 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YTs4F-0005D0-08 for categories-list@mlist.mta.ca; Fri, 06 Mar 2015 09:13:27 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8528 Archived-At: In fact this point is observed even in the original paper of Eilenberg = Mac Lane ! Furthermore, I recently proposed a notion of autocategory, a kind of = category without object ; this is a little different from categories, = and is based precisely on the distinction between four things : objects, = identities, identifiers, domains or codomains (see in CTGD in 2014), and = this allows to see with the same "eye" categories, 2-categories, etc..=20= Best, Ren=E9 Guitart Le 5 mars 2015 =E0 12:49, Uwe Egbert Wolter a =E9crit : > 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. >=20 > I know how this works. I would, however, like to have a reference. >=20 > Best >=20 > Uwe Wolter >=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]