From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6159 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Evil in bicategories Date: Mon, 13 Sep 2010 15:28:00 -0700 Message-ID: References: Reply-To: Toby Bartels 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 1284504826 2670 80.91.229.12 (14 Sep 2010 22:53:46 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 14 Sep 2010 22:53:46 +0000 (UTC) Cc: JeanBenabou , David Roberts To: categories Original-X-From: majordomo@mlist.mta.ca Wed Sep 15 00:53:45 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OveNe-0000td-Iy for gsmc-categories@m.gmane.org; Wed, 15 Sep 2010 00:53:38 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:54990) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OveM4-0003uv-Tw; Tue, 14 Sep 2010 19:52:01 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OveLu-00022i-6T for categories-list@mlist.mta.ca; Tue, 14 Sep 2010 19:51:50 -0300 Content-Disposition: inline Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6159 Archived-At: David Roberts wrote in part: >Jean B=E9nabou wrote: >>Maybe my english isn't so "beautiful", but in all cases where "evil" ha= s >>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. >Regardless of my personal convictions, I like to remain a mathematical >agnostic, so 'wrong' seems to me to be too strong. I feel the same way, which is why I *prefer* to say "evil" instead of "wr= ong". The word "evil" is so over-the-top that someone who uses it *must* be kid= ding. However, the word "wrong" sounds like it should be taken seriously, but the mathematics of strict categories is valid, not wrong at all. (It's just not the mathematics that I'm doing when I do category theory.) Incidentally, this usage of "evil" fits in with a usage of "morally" examined by Eugenia Cheng: http://www.cheng.staff.shef.ac.uk/morality/. "Morally", one cannot compare objects of a given category for equality (because the results are not preserved by an equivalence of categories); even if it is possible, it is "evil". >Toby Bartels calls categories where one is not allowed to test for >equality between arbitrary objects 'weak' and those where one can do >so 'strict' Right: http://ncatlab.org/nlab/show/strict+category In many cases, we can use "strict" instead of "evil". For example, here is David Leduc's original post: >>>In a bicategory, composition of 1-cells is associative up to >>>isomorphism. Because it would be evil to insist that h o (g o f) is >>>equal to (h o g) o f. However the source and target objects of those >>>compositions must be equal. Isn't it evil? Why not weaken this >>>requirement by saying that the sources (respectively, targets) of h o >>>(g o f) and (h o g) o f must only be isomorphic? Let us replace each usage of "evil" by "too strict": >>>In a bicategory, composition of 1-cells is associative up to >>>isomorphism. Because it would be too strict to insist that h o (g o f)= is >>>equal to (h o g) o f. However the source and target objects of those >>>compositions must be equal. Isn't it too strict? Why not weaken this >>>requirement by saying that the sources (respectively, targets) of h o >>>(g o f) and (h o g) o f must only be isomorphic? This even makes David's use of the verb "weaken" look very nice. So while I like the noun "evil" to encapsulate the whole idea (with the understanding that is not too be taken too seriously), one can probably avoid it in serious mathematical questions. (I don't mean to criticise David for using it, however.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]