From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6162 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: evil Date: Tue, 14 Sep 2010 15:50:36 +0800 Message-ID: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1284505237 4216 80.91.229.12 (14 Sep 2010 23:00:37 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 14 Sep 2010 23:00:37 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Wed Sep 15 01:00:35 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 1OveUE-00042G-Bz for gsmc-categories@m.gmane.org; Wed, 15 Sep 2010 01:00:26 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60622) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OveSs-0004ID-Ej; Tue, 14 Sep 2010 19:59:02 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OveSn-0002ET-Pw for categories-list@mlist.mta.ca; Tue, 14 Sep 2010 19:58:58 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6162 Archived-At: Sorry, if it's not too late please post this one instead: From: John Baez Date: Tue, Sep 14, 2010 at 3:33 PM Subject: Evil To: categories David wrote: Jean Benabou wrote: >> Maybe my english isn't so "beautiful", but in all cases where "evil" has >> been used, what is wrong with "wrong" instead? > I'm not so enamoured with the use of the word 'evil', but it seems to > be more entrenched than perhaps it was intended, namely as a joke. > It's supposed to be funny, but I'm glad to see it become entrenched. Why? First, it has a very specific meaning. A property of objects of some category C is said to be "evil" if it holds for some object x of C but not some isomorphic object y. More generally: a property of objects of some n-category is "evil" if it holds for some object x but not some equivalent object y. For details, see: http://ncatlab.org/nlab/show/evil Second, it captures the interesting state of affairs in category theory where some definitions can be well-formed yet somehow "suboptimal" because equations were used when isomorphisms should have been specified. "Wrong" doesn't work here, since mathematicians use it in other important ways: for example, "false", "incorrect" or "inappropriate". "Evil" is, to the best of my knowledge, never used in mathematics except in this one technical sense. If anybody finds the term "evil" upsettingly strong, I suggest "naughty" as an alternative. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]