From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2859 Path: news.gmane.org!not-for-mail From: Peter Arndt Newsgroups: gmane.science.mathematics.categories Subject: Two topos questions Date: Wed, 2 Nov 2005 03:53:43 -0300 Message-ID: <2cc0d36c0511012253p1a15630ay1c0eb35f724905db@mail.gmail.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241018947 6118 80.91.229.2 (29 Apr 2009 15:29:07 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:29:07 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Nov 2 11:58:27 2005 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 Nov 2005 11:58:27 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EXKwY-0004Mg-EG for categories-list@mta.ca; Wed, 02 Nov 2005 11:54:30 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2859 Archived-At: Hi, category theorists, 1. In a message to the categories list from 15. jan.1997 (that message can be seen at http://www.mta.ca/~cat-dist/catlist/1999/finite-topos) Lawvere talks about "the ... internal topos ... which parametrizes the decidable K-finites". Does anyone know what exactly is that internal topos? Is there some morphism that can be seen as the indexed family of decidable K-finites (just like the generic cardinal "is" the indexed family of finite cardinals and can be used to construct the full internal subcategory of finite cardinals)? 2. An object Y of a topos is said to have locally a property P if there is an object Z with global support such that Z*(Y) has the property P. For the topos of sheaves on a T1-space X (and a property P stable under pullback along subterminals), I convinced myself that this implies the existence of = a covering of X, such that P holds on the restriction of Y to each open set o= f the covering. Can this also be proved for schemes or other classes of topological spaces, maybe with additional conditions on P? Thanks a lot! Peter