From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2732 Path: news.gmane.org!not-for-mail From: Newsgroups: gmane.science.mathematics.categories Subject: preprint: Filtered colimits in the effective topos Date: Tue, 29 Jun 2004 17:52:49 +0200 (CEST) Message-ID: <200406291552.RAA22755@kodder.math.uu.nl> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018860 5526 80.91.229.2 (29 Apr 2009 15:27:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:40 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jun 29 13:33:20 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 29 Jun 2004 13:33:20 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BfLXj-00043K-00 for categories-list@mta.ca; Tue, 29 Jun 2004 13:33:11 -0300 X-Sun-Charset: US-ASCII X-Virus-Scanned: by amavisd-new at math.uu.nl Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 17 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:2732 Archived-At: A 7-page paper entitled Filtered colimits in the effective topos can be downloaded from: http://www.math.uu.nl/people/jvoosten/effcolim.ps.gz Abstract: we are concerned with the problem whether there is a small full dense subcategory in the effective topos (which would give a nice embedding of Eff into a sheaf topos). Since this topos has enough projectives, we may assume that such a category consists of the \lambda-small projectives for some cardinal \lambda. Basically, there are two theorems: 1. For \lambda regular, uncountable: the \lambda -small projectives are dense, precisely if the constant objects functor \nabla :Sets --> Eff preserves \lambda-filtered colimits. 2. \nabla : Sets --> Eff does not preserve \omega _1-filtered colimits (hence, by 1., the countable projectives are not dense). Jaap van Oosten