From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8540 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Category without objects Date: Tue, 10 Mar 2015 21:20:39 -0700 Message-ID: References: , Reply-To: Vaughan Pratt NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1426116689 19838 80.91.229.3 (11 Mar 2015 23:31:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 11 Mar 2015 23:31:29 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Thu Mar 12 00:31:21 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 1YVq5w-0006l4-HR for gsmc-categories@m.gmane.org; Thu, 12 Mar 2015 00:31:21 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35352) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1YVq4v-0007zh-Nw; Wed, 11 Mar 2015 20:30:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1YVq4w-0002zf-2Y for categories-list@mlist.mta.ca; Wed, 11 Mar 2015 20:30:18 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8540 Archived-At: On 08/03/2015 19:53, F. William Lawvere wrote: > It is difficult to understand "without objects" without any definition > of "object". One could raise an analogous objection to the notion of a "reflexive graph without vertices", defined as an M-set for the 3-element monoid M consisting of the monotone endomorphisms of the poset 0 < 1. While no mention is made of vertices in this definition, an equivalent notion arises in a canonical way by taking the Karoubi envelope of M, yielding a notion of "vertex". "Without vertices" then just means economizing by skipping the step of taking the envelope. Quine wrote "Word and Object". Reasoning analogously as above, what a category theorist would call an object, Quine would call a word. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]