From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1018 Path: news.gmane.org!not-for-mail From: F W Lawvere Newsgroups: gmane.science.mathematics.categories Subject: Re: Pullback perserving functor Date: Fri, 29 Jan 1999 09:51:13 -0500 (EST) Message-ID: References: Reply-To: wlawvere@ACSU.Buffalo.EDU NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017481 29011 80.91.229.2 (29 Apr 2009 15:04:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:04:41 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Fri Jan 29 23:09:59 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id WAA10073 for categories-list; Fri, 29 Jan 1999 22:20:37 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 38 Xref: news.gmane.org gmane.science.mathematics.categories:1018 Archived-At: Whether or not these functors form a cartesian-closed category depends strongly on the nature of the domain category. For example, if the domain category is an abelian category as opposed to it being a pretopos. Related matters are discussed in the recent paper by Borceux and Pedicchio and the papers there cited: Left-exact presheaves on a small pretopos, Journal of Pure and Applied Algebra, vol. 135, no. 1, 4 Febr. 1999, pp 9 - 22. ******************************************************************************* F. William Lawvere Mathematics Dept. SUNY wlawvere@acsu.buffalo.edu 106 Diefendorf Hall 716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA ******************************************************************************* On Thu, 28 Jan 1999, Hongseok Yang wrote: > > Would someone let me know the answer and the proof or counter example of > the following question? > > Suppose the category C has a pullback for every pair of morphism > (f : X -> Y, g : W -> Y). Let K be the full subcategory of the functor > category Func(C,Set) whose objects are pullback perserving functors. > Is K ccc? (If so, how I can show this?) > > Thanks, > Hongseok > > >