From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1863 Path: news.gmane.org!not-for-mail From: Danilov Nikita Newsgroups: gmane.science.mathematics.categories Subject: Re: Which is the simplest example? Date: Fri, 16 Feb 2001 21:18:44 +0300 Message-ID: <14989.28420.518530.766264@beta.namesys.com> References: <200102161343.f1GDhuo24693@saul.cis.upenn.edu> 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 1241018159 860 80.91.229.2 (29 Apr 2009 15:15:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:59 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Feb 17 15:04:29 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f1HIU7u14568 for categories-list; Sat, 17 Feb 2001 14:30:07 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: beta.namesys.com: god set sender to NikitaDanilov@Yahoo.COM using -f In-Reply-To: <200102161343.f1GDhuo24693@saul.cis.upenn.edu> X-Mailer: VM 6.89 under 21.1 (patch 8) "Bryce Canyon" XEmacs Lucid Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 45 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:1863 Archived-At: Peter Freyd writes: > I said that the simplest example of a category with pullbacks but not > products is the discrete category with two objects. Come to think of > it, any category with exactly two morphisms is an example. Initial question was If a category C has pullbacs no terminal object, then has C finite product? Now, think of empty category (one without objects and morphisms): (*) it doesn't contain terminal object (*) it does have pullbacks of all pairs of objects (because there are none) (*) it doesn't contain all finite products (as it doesn't contain limit of empty diagram---terminal object) Now, simplify _this_ counter-example. :) Actually, if terminal object is considered as product of zero multipliers (as it's usually does), then initial question contains answer in itself. Nikita.