From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2057 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: infinite trees Date: Fri, 14 Dec 2001 12:29:49 +0100 (MET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018373 2228 80.91.229.2 (29 Apr 2009 15:19:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:33 +0000 (UTC) To: categories net Original-X-From: rrosebru@mta.ca Fri Dec 14 09:01:35 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 14 Dec 2001 09:01:35 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16EriE-0002UY-00 for categories-list@mta.ca; Fri, 14 Dec 2001 08:45:14 -0400 X-Sender: adamek@lisa Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 30 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2057 Archived-At: What is actually a first reference for the fact that for every polynomial endofunctor of Set a final coalgebra consists of all properly labelled (finite and infinite) trees? I suspect the first authors to study this were Arbib and Manes in their "Parametrized data types do not need...", Information and control 52 (1982), 139-158. However, it is obvious from that paper that Arbib and Manes were definitely unaware of the general statement, which explains why they only mention some special cases in their book in 1986. Jiri Adamek xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx