From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5591 Path: news.gmane.org!not-for-mail From: Partha Pratim Ghosh Newsgroups: gmane.science.mathematics.categories Subject: Re: abstraction of notation from sets. Date: Thu, 25 Feb 2010 07:17:12 +0000 (UTC) Message-ID: References: Reply-To: Partha Pratim Ghosh NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1267105587 6891 80.91.229.12 (25 Feb 2010 13:46:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 25 Feb 2010 13:46:27 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Thu Feb 25 14:46:23 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 4.69) (envelope-from ) id 1Nke2p-0004NZ-5H for gsmc-categories@m.gmane.org; Thu, 25 Feb 2010 14:46:23 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NkdZk-000517-LM for categories-list@mta.ca; Thu, 25 Feb 2010 09:16:20 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5591 Archived-At: shaw.ca> writes: > > When S is a set, the notation "a \epsilon S" is familiar. > Is this ever extended to CT? All the texts I recall use > natural language such as "A is an object of C". What if > a more symbolic notation is required? > > Thanks, ... Peter E. > Dear Peter, There are two types of entities, one called objects and the other called arrows. However, there are ways to deal away with objects, and one could only consider the arrows, in which case although in my opinion the presentation becomes much more formal and less intuitive (?!), one could easily import the symbols of $\epsilon$; alternatively, one could formulate two classes (one for objects and other for arrows) and do a similar import; or else one could use a type theoretic fashion, say "A.Obj" to denote an instance of objects and "A.Arr" to denote an instance of arrows, and so on. Yet, in some form or the other one could do this...., but I ponder: why? Thus, I could not quite understand the intent of your question. Please could you elaborate on this. With my regards, partha [For admin and other information see: http://www.mta.ca/~cat-dist/ ]