From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2003 Path: news.gmane.org!not-for-mail From: Dusko Pavlovic Newsgroups: gmane.science.mathematics.categories Subject: Re: co-iteration? Date: Thu, 07 Jun 2001 00:10:24 -0700 Message-ID: <3B1F28E0.9B1C8469@kestrel.edu> References: <014201c0ee9f$053516f0$060a000a@AVILCIUS> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii; x-mac-type="54455854"; x-mac-creator="4D4F5353" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018275 1679 80.91.229.2 (29 Apr 2009 15:17:55 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:55 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Jun 7 04:31:40 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f576trw01561 for categories-list; Thu, 7 Jun 2001 03:55:53 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.75C-CCK-MCD {C-UDP; EBM-APPLE} (Macintosh; U; PPC) X-Accept-Language: en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:2003 Archived-At: > 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" [...] > 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? by reversing the arrows, and replacing coproducts by products, we get that, for the function g:AxB->A holds B---->AxB--g-->A = B--g'-->A, ie g(g'(y),y) = g'(y) in words, the "coiterator" g' is just a fixpoint of g. -- dusko