From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5586 Path: news.gmane.org!not-for-mail From: Mikael Vejdemo-Johansson Newsgroups: gmane.science.mathematics.categories Subject: Re: abstraction of notation from sets. Date: Wed, 24 Feb 2010 07:59:06 -0800 Message-ID: References: Reply-To: Mikael Vejdemo-Johansson NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1267105435 6329 80.91.229.12 (25 Feb 2010 13:43:55 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 25 Feb 2010 13:43:55 +0000 (UTC) To: peasthope@shaw.ca, categories@mta.ca Original-X-From: categories@mta.ca Thu Feb 25 14:43:51 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 1Nke0K-00035D-4u for gsmc-categories@m.gmane.org; Thu, 25 Feb 2010 14:43:48 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NkdW3-0004lN-9v for categories-list@mta.ca; Thu, 25 Feb 2010 09:12:31 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5586 Archived-At: On Feb 23, 2010, at 4:43 PM, peasthope@shaw.ca wrote: > 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? > I've seen $a \in Ob(C)$ numerous times, and also - though primarily from Barr & Wells - $a \in C_0$, with the rationale that a category is a graph (consisting of vertices C_0 and edges C_1), with extra conditions introduced to capture the composition operation, showing up as functions defined on composable sequences C_n of n edges (most often for n=2, or 3 for associativity). -- Mikael Vejdemo Johansson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]