From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9864 Path: news.gmane.org!.POSTED.blaine.gmane.org!not-for-mail From: "Michael Barr, Prof." Newsgroups: gmane.science.mathematics.categories Subject: Question on simplicial homotopies Date: Mon, 18 Mar 2019 19:10:29 +0000 Message-ID: Reply-To: "Michael Barr, Prof." Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Injection-Info: blaine.gmane.org; posting-host="blaine.gmane.org:195.159.176.226"; logging-data="247969"; mail-complaints-to="usenet@blaine.gmane.org" To: "categories@mta.ca list" Original-X-From: majordomo@mlist.mta.ca Tue Mar 19 00:56:05 2019 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by blaine.gmane.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.89) (envelope-from ) id 1h626s-0012HZ-Om for gsmc-categories@m.gmane.org; Tue, 19 Mar 2019 00:56:02 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59119) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1h627K-0001rH-7S; Mon, 18 Mar 2019 20:56:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1h625Z-0006Vh-Qg for categories-list@mlist.mta.ca; Mon, 18 Mar 2019 20:54:41 -0300 Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9864 Archived-At: Most of you know the combinatorial definition of simplicial homotopy in ter= ms of families h^i: X_n --> Y_{n+1} satisfying a number of identities, incl= uding d^0h^0 =3D f_n and d^{n+1}h^n =3D g_n, to define a homotopy from f to= g. We (John Kennison, Bob Raphael, and I) have been using a notion we cal= l reduced homotopy which consists in a series of maps r^i: X_n --> Y_n sati= sfying certain identities. It turns out that the r^i =3D d^{i+1}h^i =3D d^= ih^i (for all except the extreme values of i, 0 and n+1 when only the one o= r the other is defined) carry all the information and can have technical ad= vantages in certain cases. What I would like to know is whether they appea= r anywhere in the literature that can be referred to. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]