From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1738 Path: news.gmane.org!not-for-mail From: Tom Leinster Newsgroups: gmane.science.mathematics.categories Subject: Reals as final coalgebra (exercise) Date: Tue, 5 Dec 2000 19:55:56 +0000 (GMT) Message-ID: 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 1241018056 32678 80.91.229.2 (29 Apr 2009 15:14:16 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:16 +0000 (UTC) Cc: T.Leinster@dpmms.cam.ac.uk (Tom Leinster) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Dec 5 20:50:10 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eB5Nuop22119 for categories-list; Tue, 5 Dec 2000 19:56:50 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: ELM [version 2.5 PL3] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 11 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:1738 Archived-At: Fans of the characterization of the real interval as a final coalgebra might be interested to see the exercise I set the Part III (first year graduate) students in Cambridge taking this year's Category Theory course. It's a bit too cumbersome to reproduce in plain text, but can be found as the last question on sheet 3 at http://www.dpmms.cam.ac.uk/~leinster/categories and consists of a guided proof of the fact that the closed real interval is terminal in a certain category of coalgebras. I tried to make the exercise as quick and easy as possible, which is why there is no mention of the wedge product, nor orderings, nor digital expansions. I don't know whether this (particularly the omission of the wedge) is at some cost to understanding. If anyone has any suggestions as to how the exercise might be made more transparent then I'd be interested to hear; I'm aware that there are plenty of people on this list who have a deeper understanding of this result than I do. Flagged "highly optional" as it was, no-one as far as I'm aware has actually tried *doing* this question... Tom