From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4802 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: terminology in definitions of limits Date: Tue, 20 Jan 2009 23:34:48 -0800 Message-ID: Reply-To: Vaughan Pratt NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020182 14900 80.91.229.2 (29 Apr 2009 15:49:42 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:49:42 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jan 21 09:04:18 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 21 Jan 2009 09:04:18 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LPcka-0000KM-Pc for categories-list@mta.ca; Wed, 21 Jan 2009 09:04:08 -0400 Original-Sender: categories@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:4802 Archived-At: Colin McLarty wrote: > I often call them "test objects" in talking with students (by analogy > with "test particles" in General Relativity). I don't think I have ever > done it in print. But I did use "T" as the typical name of such an > object in my book. > > I am curious to know what others think. From a game-theoretic standpoint one can be either taking the test or administering it. Both sides call it the test, showing that the name is stable under perp (change of team). However that's not to say that "test" gives a helpful perspective in either case. A right adjoint defined by its adjunction is simply a specification of *all* homsets to it, and dually, in the case of left adjoints, of all the homsets from it. What you're calling a "test" object there is for me merely the variable being universally quantified over in the definition of "all." Whether a student is going to find it helpful thinking of a universally quantified variable as a "test object" is going to be less a question of what the student thinks about that perspective than what the teacher thinks about it and whether they can convey their point of view. The mathematically talented student who immediately sees it is merely being universally quantified over may be more puzzled than helped. But then how many of us are so lucky as to have a significant number of mathematically talented students in our classes? Vaughan