From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6283 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: The omega-functor omega-category Date: Mon, 04 Oct 2010 00:52:31 -0700 Message-ID: References: Reply-To: Vaughan Pratt 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: dough.gmane.org 1286194360 26076 80.91.229.12 (4 Oct 2010 12:12:40 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 4 Oct 2010 12:12:40 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Mon Oct 04 14:12:38 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1P2juI-00018R-KQ for gsmc-categories@m.gmane.org; Mon, 04 Oct 2010 14:12:38 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48360) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P2jta-0007os-1W; Mon, 04 Oct 2010 09:11:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P2jtX-0001ms-Bh for categories-list@mlist.mta.ca; Mon, 04 Oct 2010 09:11:51 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6283 Archived-At: On 10/2/2010 3:03 PM, Michael Shulman wrote: > I personally prefer to say that "unique choice structure" is something > "in between" property and structure. Kelly and Lack dubbed it > "Property-like structure" in their paper with that title. The > difference is exactly as you say: property-like structure is unique > (up to unique isomorphism) when it exists, but is not necessarily > "preserved" by all morphisms. How should this terminology be applied when the property-like structure is necessarily preserved by all morphisms? A group can be defined as a monoid with the property that all of its elements have inverses. The inverse is preserved by all morphisms. A Boolean algebra can be defined as a bounded distributive lattice with the property that all of its elements have complements. The complement is preserved by all morphisms. Are these merely "property-like structures," or are they actual structures, despite being defined merely as properties? Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]