From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1618 Path: news.gmane.org!not-for-mail From: Tobias Schroeder Newsgroups: gmane.science.mathematics.categories Subject: Pullback preserving Set-functors Date: Mon, 11 Sep 2000 15:39:51 +0200 (MET DST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241017970 32091 80.91.229.2 (29 Apr 2009 15:12:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:12:50 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Sep 11 12:48:21 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id LAA25253 for categories-list; Mon, 11 Sep 2000 11:48:57 -0300 (ADT) X-Authentication-Warning: shaula.Mathematik.Uni-Marburg.DE: tschroed owned process doing -bs X-Sender: tschroed@shaula X-MIME-Autoconverted: from QUOTED-PRINTABLE to 8bit by mailserv.mta.ca id KAA25210 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 46 Xref: news.gmane.org gmane.science.mathematics.categories:1618 Archived-At: I'm interested in proofs of or counterexamples for the following conjectures: Conjecture 1: Any Set-endofunctor that preserves kernels (i.e. pullbacks of a mapping with itself) preserves pullbacks. Conjecture 2: Any Set-endofunctor that preserves kernels *and inverse images* (i.e. pullbacks where one of the mapping is injective) preserves pullbacks. Conjecture 3: Same as Conj. 2 with *and inverse images* replaced by *and equalizers*. Conjecture 4: Same as Conj. 1-3, but concerning *weak* preservation. Conjectur 5: Same as 1-4, but for Set-endofunctors that are subfunctors of a pullback preserving functor. I tried to prove these facts in several ways but was not able to do it or to find a counterexample (the answer to this questions is of some relevance for my work on coalgebras) ... and it looks quite easy, doesn't it? Can somebody help me in this? Thank you very much in advance Tobias Schröder -------------------------------------------------------------- Tobias Schröder FB Mathematik und Informatik Philipps-Universität Marburg WWW: http://www.mathematik.uni-marburg.de/~tschroed email: tschroed@mathematik.uni-marburg.de