From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5820 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re terminology: Date: Wed, 19 May 2010 11:38:09 +0100 Message-ID: Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1274315049 2936 80.91.229.12 (20 May 2010 00:24:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 20 May 2010 00:24:09 +0000 (UTC) To: "categories@mta.ca" Original-X-From: categories@mta.ca Thu May 20 02:24:08 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OEtYW-0008Tq-9v for gsmc-categories@m.gmane.org; Thu, 20 May 2010 02:24:08 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OEt8E-00071o-4W for categories-list@mta.ca; Wed, 19 May 2010 20:56:58 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5820 Archived-At: Peter Sellinger writes recently:=20 --------------------------------------------------- I think this is a very apt illustration of what happens if a term with an existing meaning is redefined to mean something else. Henceforth it is impossible for anybody to use the term (with either meaning) without first giving a definition. --------------------------------------------------- I completely agree. My own problem is with term `infinity groupoid' which= is used to describe something which is not even a groupoid, and whose us= e seems to me to militate against the understanding of what has been achi= eved with the original and much earlier definition. I once asked Gian-Car= l Rota about such change of terminology, in connection with a refereeing = job, and he agreed that mathematicians are used to creating confusion in = this way.=20 There are two easy tendencies: one is to use an old name in a quite diffe= rent way, and the other is to use a new name for an old idea, so that the= use of the old term looks old fashioned, and a lot of work may be consig= ned to the dustbin of history, becoming not easy of access for new stude= nts.=20 It seems to be an example of these confusions is the way the simplicial s= ingular complex of a space is called an infinity-groupoid, even the `fund= amental infinity groupoid', when what seems to be referred to is that it = is a Kan complex, i.e. satisfies the Kan extension condition, studied sin= ce 1955. The new term sounds like `dressing up' an old idea to look new. = My personal objection to this change of terminology (i.e. axe to grind!) = is that this distracts from studying the not so simple proofs that strict= higher homotopical structures exist, which mainly are for structured spa= ces (in particular filtered spaces (Brown/Higgins, Ashley), n-cubes of sp= aces (Loday), and more recently smooth spaces (Faria Martins/Picken)). Th= e analysis and comparison of these uses should be made. It was certainly = a relief to Philip and I that we could do something with filtered spaces = which we could not do for the absolute case; the significance of the fact= that these constructions work and lead to specific calculations should b= e thought about.=20 The term `higher dimensional group theory' which was published in a paper= with that title in 1982 was intended to suggest developing higher groupo= id theory and its relations to homotopy theory in the spirit of group the= ory, which meant specific constructions relevant to geometry and calculat= ions, even computer calculations, of many examples, in which actual numb= ers arise as a test of and examples of the general theory, and in which s= ome aspects of group theory are sensibly seen as better represented in th= e higher dimensional theory; and example of this is the nonabelian tensor= product of groups, where group theorists have found lots of pickings.=20 I am not sure how these terminological problems will be resolved, and I k= now the term (\infty,n)-groupoid has been well used recently but the prob= lem of relation to the older ideas, which have had a certain success, sho= uld be recognised.=20 Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]