From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1975 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: connected functors and pseudoepis Date: Fri, 25 May 2001 12:34:04 +0200 (MET DST) Message-ID: <200105251034.MAA03907@lisa.iti.cs.tu-bs.de> 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 1241018245 1502 80.91.229.2 (29 Apr 2009 15:17:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:25 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri May 25 08:23:57 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4PAaDe11642 for categories-list; Fri, 25 May 2001 07:36:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: ELM [version 2.5 PL2] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 43 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:1975 Archived-At: The connected functors we have mentioned the other day, i.e. those functors p: E -> B for which (-).p Set^B -> Set^E is fully faithful, are easily seen to be precisely the lax epimorphisms of the 2-category Cat (of small categories). We do not know whether every pseudoepimorphism in Cat is connected, does anyone know? The answer is affirmative if B is a preorder. J.Adamek, R. El Bashir, M. Sobral and J. Velebil xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx