From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4809 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: terminology in definitions of limits Date: Thu, 22 Jan 2009 11:17:36 +0000 (GMT) Message-ID: Reply-To: Richard Garner NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241020186 14934 80.91.229.2 (29 Apr 2009 15:49:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:49:46 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Jan 22 22:29:21 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:29:21 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBgm-0002P5-Cx for categories-list@mta.ca; Thu, 22 Jan 2009 22:22:32 -0400 Original-Sender: categories@mta.ca Precedence: bulk X-Keywords: X-UID: 30 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:4809 Archived-At: I have always used the phrase "test object" in a slightly different sense. Namely, to refer to a tractably small collection of objects that one may use, not only to detect, but also to calculate some right adjoint. Thus in Set, one may take the terminal object; in Set/X, the elements 1-->X; in Cat, the ordinals 1, 2 and 3; in presheaf categories, the representables; and so on. The best case is that these test objects are colimit dense, since then your calculations always yield a right adjoint as soon as the functor you start with preserves colimits. Richard