From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/249 Path: news.gmane.org!not-for-mail From: Pierre Cardascia Newsgroups: gmane.science.mathematics.categories Subject: A theorem from Herrlich and Strecker Date: Wed, 15 Apr 2009 19:35:34 +0000 (GMT) Message-ID: Reply-To: Pierre Cardascia NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1239893659 10949 80.91.229.12 (16 Apr 2009 14:54:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 16 Apr 2009 14:54:19 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Thu Apr 16 16:55:38 2009 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 4.50) id 1LuSzm-0000dB-CY for gsmc-categories@m.gmane.org; Thu, 16 Apr 2009 16:55:18 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LuSJD-0000YZ-Cj for categories-list@mta.ca; Thu, 16 Apr 2009 11:11:19 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:249 Archived-At: Dear Cat=E9goristes,=0A=0AI'm working on an introduction for categorical lo= gic, and I try to avoid using the notion of limit before introducing the no= tion of functor in my work (because limit means limit of functors. Squarely= , we can introduce the limit before, but we don't understand why the limit = is called limit, and limit of what ??).=0ABut I have to introduce the notio= n of categories finitely complete. SO I think about this theorem :=0A=3D=3D= =3D> If C has a terminal object, and a pullback for each pair of arrows wit= h common codomains, then C is finitively complete.=0AI found that without a= ny proof in Goldblatt. Rob Goldblatt just said : "you can find it into such= book from Herrlich and Strecker"... Does somebody has the proof ? Can I us= e this theorem to define complety closed categories instead of working with= limits ? Or does somebody have any way to define complety closed categorie= s without any reference to functors ?=0A=0AThanks !=0A=0APierre CARDASCIA= =0A=0A=0A