From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3030 Path: news.gmane.org!not-for-mail From: Philippe Gaucher Newsgroups: gmane.science.mathematics.categories Subject: Bibliographical reference needed Date: Tue, 14 Feb 2006 12:52:32 +0100 Message-ID: Reply-To: gaucher@pps.jussieu.fr NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019054 6950 80.91.229.2 (29 Apr 2009 15:30:54 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:54 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Feb 14 20:28:25 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 14 Feb 2006 20:28:25 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1F9ANH-0003EC-J5 for categories-list@mta.ca; Tue, 14 Feb 2006 20:18:27 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:3030 Archived-At: Dear All, I would need please a bibliographical reference for the following fact : "Let C be a complete cocomplete cartesian closed category. Let I be a small category. Then the category of functors C^I is cartesian closed." (If Hom is the internal hom functor of C, let Hom(X_*,Y_*)=\int_i Hom(X_i,Y_i) ; then the internal hom of C^I is defined by HOM(X_*,Y_*)_j= j |-> Hom(X_* x 1[j], Y_*) where 1 is the terminal object of C and Z |-> Z[j] is left adjoint to the i-th evaluation functor X_* |-> X_j) Thanks in advance. pg.