From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2053 Path: news.gmane.org!not-for-mail From: JAMES STASHEFF Newsgroups: gmane.science.mathematics.categories Subject: Re: Defining monoids Date: Sun, 9 Dec 2001 20:35:20 -0500 (EST) Message-ID: References: <5.1.0.14.2.20011206155739.0204cd50@mail.oberlin.net> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018370 2214 80.91.229.2 (29 Apr 2009 15:19:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:30 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Dec 10 10:17:29 2001 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 10 Dec 2001 10:17:29 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 3.33 #2) id 16DRBL-0003Ew-00 for categories-list@mta.ca; Mon, 10 Dec 2001 10:13:23 -0400 X-Sender: stasheff@login3.isis.unc.edu In-Reply-To: <5.1.0.14.2.20011206155739.0204cd50@mail.oberlin.net> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 26 Original-Lines: 53 Xref: news.gmane.org gmane.science.mathematics.categories:2053 Archived-At: For those who prefer to see the forests and the trees, that point of view is prominent in the operad/modad/monoidal interaction. Much such material will be in our book on Operads (Markl and Shnider and me) .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds On Thu, 6 Dec 2001, Charles Wells wrote: > > > In talking about defining monoids, Toby Bartels wrote: > > "We could also go straight to trees and define them as the basic operations, > then requiring as axiom that grafting of trees produces the same result > as composing the operations." > > This is the mu operation of the corresponding monad. Every single-sorted > "idea" in the sense of the recent discussion generates a monad in sets with > a mu like this. For each set S there is a set of possible computations TS, > a mu:TTS to TS, and a "OneIdentity" operation in the sense of Mathematica > that says the computation consisting of a single node results in that node; > these subject to the monad laws. In other words, the phenomenon you noted > is an instance of a general result. > > --Charles Wells > > Charles Wells, > Emeritus Professor of Mathematics, Case Western Reserve University > Affiliate Scholar, Oberlin College > Send all mail to: > 105 South Cedar St., Oberlin, Ohio 44074, USA. > email: charles@freude.com. > home phone: 440 774 1926. > professional website: http://www.cwru.edu/artsci/math/wells/home.html > personal website: http://www.oberlin.net/~cwells/index.html > genealogical website: > http://familytreemaker.genealogy.com/users/w/e/l/Charles-Wells/ > NE Ohio Sacred Harp website: http://www.oberlin.net/~cwells/sh.htm > > > > >