From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2475 Path: news.gmane.org!not-for-mail From: James Stasheff Newsgroups: gmane.science.mathematics.categories Subject: terminology Date: Thu, 16 Oct 2003 17:39:27 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018685 4326 80.91.229.2 (29 Apr 2009 15:24:45 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:45 +0000 (UTC) To: dmd1@lehigh.edu, categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Oct 17 09:22:21 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 17 Oct 2003 09:22:21 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1AATaq-0000mV-00 for categories-list@mta.ca; Fri, 17 Oct 2003 09:20:32 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 26 Original-Lines: 50 Xref: news.gmane.org gmane.science.mathematics.categories:2475 Archived-At: In `higher homotopy theory', terminology has not setled down nor is it transparent homotopy ___________ algebra can mean a variety of things letting ______________ = associative it can mean JUST that there is a homtopy for associaitivity or some authors use it to mean A_\infty which I initially tried to indicate by strongly homtopy associative _\infty seems to have caught on to mean the presence of higher homtopies of all orders in most but not all cases, such algebras have a homtopy invariant defintion so I would suggest the following revisionist terminology 1-homotopy associative means JUST that there is a homotopy for associaitivity similarly n-homotopy associative would mean homotopies of homotopies of... homotopy invariant ___ algebra would mean just what it says so far so good but now what about e.g. 1-homotopy associaitve satisfying a STRICT pentagon?? perhaps strict 1-homotopy open to suggestions Jim Stasheff jds@math.upenn.edu Home page: www.math.unc.edu/Faculty/jds As of July 1, 2002, I am Professor Emeritus at UNC and I will be visiting U Penn but for hard copy the relevant address is: 146 Woodland Dr Lansdale PA 19446 (215)822-6707