From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2000 Path: news.gmane.org!not-for-mail From: "Al Vilcius" Newsgroups: gmane.science.mathematics.categories Subject: co-iteration? Date: Wed, 6 Jun 2001 11:40:31 -0400 Message-ID: <014201c0ee9f$053516f0$060a000a@AVILCIUS> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 X-Trace: ger.gmane.org 1241018272 1664 80.91.229.2 (29 Apr 2009 15:17:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:52 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Jun 6 22:05:55 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f570UFr29494 for categories-list; Wed, 6 Jun 2001 21:30:15 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 10 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:2000 Archived-At: For many (categorical) notions, there is a useful (often fantastic) dual notion. What about iteration? In a category with finite coproducts, we have a notion of iteration f:A-->A+B (written A -f-> A+B here) which in the case of sets and partial functions, for example, is completely specified by the Elgot equation A -f-> A+B -f"+1-> B = A -f"-> B recursive in f" (plus one more little, quite natural condition - see [Manes '92]) This awful looking mess, written using the infix morphism notation, actually looks quite neat when you draw the diagram. Now without meaning to start the "co"-wars again, - is there a useful notion of co-iteration? - what could it do for us, say in the category of partial functions? - is there a simple algebra/coalgebra context? Reference: [Manes '92] E.G.Manes, "Predicate Transformer Semantics", CUP 1992 Al Vilcius personal: al.r@vilcius.com business: avilcius@webpearls.com