From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5828 Path: news.gmane.org!not-for-mail From: Joyal@mta.ca, Andre Newsgroups: gmane.science.mathematics.categories Subject: Re terminology: Date: Thu, 20 May 2010 18:15:04 -0400 Message-ID: References: Reply-To: Joyal@mta.ca, Andre NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1274454504 11120 80.91.229.12 (21 May 2010 15:08:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 21 May 2010 15:08:24 +0000 (UTC) To: , "Ronnie Brown" , Original-X-From: categories@mta.ca Fri May 21 17:08:20 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 1OFTpj-0007HJ-P0 for gsmc-categories@m.gmane.org; Fri, 21 May 2010 17:08:20 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OFTAz-0003PL-6L for categories-list@mta.ca; Fri, 21 May 2010 11:26:13 -0300 Thread-Index: Acr4Vm2t54taDTFLQxGnzPOEbs55cwABMovL Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5828 Archived-At: Dear Urs and Ronnie, Sergei Soloviev wrote: >My personal opinion is that this process is very much influenced >by the pressure of "bibliometry", "impact factors" and other "modern >trends" - people often not very scrupulously invent and reinvent >terminology to be better cited, and, conscious or not, it often very >much smells of imposture. Urs Schreiber wrote: =20 >It seems to follow the well established terminology in higher category >theory, which proceeds: category, 2-category, 3-category, .... >infinity-category and groupoid, 2-groupoid, 3-groupoid, ... >infinity-groupoid. I introduced the terminology "quasi-category" as an alternative name=20 for weak Kan complexes because I wanted to suggest that the theory of = these objects=20 was closer to category theory than to the theory of Kan complexes. For example, the notion of an initial object in a quasi-category=20 is very important, like that of initial object in a category. But only a contractible Kan complex can have an initial object.=20 The theory of quasi-categories turns out to be amazingly close to = category theory despite the fact that its natural setting is simplicial homotopy theory. The name "quasi-category" is for me less frightening than "infinity-category" which has the name of God into it. More seriously, why should we attach the prefix "infinity" to an object=20 which is no more endless than the set of natural numbers, or the set of = rational numbers,=20 or the simplicial category Delta? The terminology could be reflecting = the (relative) failure of the algebraic approach to higher categories. An algebraic description of homotopy type of the 2-sphere is missing and it could be endless. But the 2-sphere is easy to describe = simplicially:=20 S^2=3D Delta[2]/partial \Delta[2] Best,=20 Andr=E9 =20 -------- Message d'origine-------- De: categories@mta.ca de la part de soloviev@irit.fr Date: jeu. 20/05/2010 03:58 =C0: Ronnie Brown Objet : categories: Re terminology: =20 My personal opinion is that this process is very much influenced by the pressure of "bibliometry", "impact factors" and other "modern trends" - people often not very scrupulously invent and reinvent terminology to be better cited, and, conscious or not, it often very much smells of imposture. Sergei Soloviev [For admin and other information see: http://www.mta.ca/~cat-dist/ ]