From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6206 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: are fibrations evil? Date: Wed, 22 Sep 2010 15:56:22 -0300 Message-ID: References: <20100922025245.GA14958@ugcs.caltech.edu> Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1285330947 814 80.91.229.12 (24 Sep 2010 12:22:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 24 Sep 2010 12:22:27 +0000 (UTC) Cc: categories To: Toby Bartels Original-X-From: majordomo@mlist.mta.ca Fri Sep 24 14:22:25 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Oz7IG-0000Se-DR for gsmc-categories@m.gmane.org; Fri, 24 Sep 2010 14:22:24 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:59804) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Oz7HL-0005py-2o; Fri, 24 Sep 2010 09:21:27 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Oz7HF-0001j2-25 for categories-list@mlist.mta.ca; Fri, 24 Sep 2010 09:21:21 -0300 In-Reply-To: <20100922025245.GA14958@ugcs.caltech.edu> Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6206 Archived-At: Toby Bartels wrote: > > Shall we stop saying "natural" and say "invariant under composition"? > Or is that term allowed under the grandfather clause, > since it was being used imprecisely before category theory defined it? Dear Toby, your choice of example is very unfortunate. Mac Lane wrote that category theory was invented to define functor, and that functor was invented to define "natural" transformation. How do you compare the importance of the concepts "invariant under composition" (assuming that is the definition of "natural") and "invariant under equivalence". The discovery of the property underneath many important mathematical developments (property not clearly evident or identified at the time) (like Stone duality just one example) was an extraordinary accomplishment. Invariant under equivalence is obviously used, is a concept already there (whether true or false). The introduction of a new name for it can only be justified by a frequent use, which is not clear at the moment. > If I can find a citation where John Baez used the term "evil" > before he knew how to define it, will that make it OK? > Or is that irrelevant because John was already working in the ghetto? ????????????? > You may continue to write down strict definitions, > and we will continue to weaken them as we need. > Different styles of mathematics are not at war. Sorry, I never said that i will only write strict definitions (as a matter of fact I have already written several non strict ones when I need them and they were naturally the correct ones over the strict version). If I run into a concept (or definition) non invariant under equivalence, I will just say so. No need to introduce a name for it, and much worse to call it "evil". Understand ? > I understand that "evil" is grating; other terms have been suggested. > But no, *any* short term to replace "not invariant under equivalence" > is forbidden by your decree: it relegates us to the ghetto. > Well, that is your interpretation, but it doesn't affect my mathematics. Your mathematics will not change a bit whether you use the term "evil", or any other term "x", or simply "not invariant under equivalence". e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]