From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1812 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Michael Healy's question on math and AI Date: Sat, 27 Jan 2001 19:07:58 -0500 (EST) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018120 598 80.91.229.2 (29 Apr 2009 15:15:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:20 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Jan 29 10:51:42 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f0TDWSU30457 for categories-list; Mon, 29 Jan 2001 09:32:28 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca In-Reply-To: Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 43 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:1812 Archived-At: I mean the initial algebra for the theory with a nullary operation 0:1 --> N and a unary operation s:N --> N. 1 stands for the terminal object (empty product). On Sun, 28 Jan 2001, Bill Halchin wrote: > > > >For another example, consider the traditional definition of Z as the set > >{0,{0},{0,{0}},{0,{0}{0,{0}}},...} > >and contrast that to the categorical specification. > ^^^ Michael, to make things more explicit I take you > mean the category with one object N and two arrows, 0 & S, > such that > > 0:N->N and s:N->N > > Yes? > > Regards, > > Bill Halchin