From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5481 Path: news.gmane.org!not-for-mail From: David Yetter Newsgroups: gmane.science.mathematics.categories Subject: Re: evil Date: Wed, 06 Jan 2010 12:43:40 -0600 Message-ID: References: Reply-To: David Yetter NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1262833840 31874 80.91.229.12 (7 Jan 2010 03:10:40 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 7 Jan 2010 03:10:40 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Thu Jan 07 04:10:31 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from [138.73.1.1] (helo=mailserv.mta.ca) by lo.gmane.org with esmtp (Exim 4.50) id 1NSila-0005fd-Cj for gsmc-categories@m.gmane.org; Thu, 07 Jan 2010 04:10:30 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NSiNG-0000mL-77 for categories-list@mta.ca; Wed, 06 Jan 2010 22:45:22 -0400 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5481 Archived-At: I have been following with some amusement the discussion of 'evil'. I am mostly amused because long ago, I think in my grad student days standing in Peter Freyd's office, I had made the suggestion that to avoid overloading adjectives (normal and regular being particularly abominable examples of the phenomenon) mathematicians should resort to using adjectives that usually have a moral denotation. Once one realizes that 'evil' exists not just for objects in categories, but for 0- and 1-arrows in bicategories, 0-, 1- and 2-arrows in tricategories, . . . it seems to me the proper attitude to take toward 'evil' (or strictness) is given by Saunders' dictum about generality: "good general theory does not search for the maximum generality, but for the right generality". So a good (higher) categorical structure should not search for the maximum weakness, but for the right weakness. (Or, if you want, not search for the minimum 'evil', but the the right amount of 'evil'.) For instance, it seems to me that structure of the category of framed tangles in which arrows are ambient isotopy classes (rel boundary) of framed tangles, which Shum's beautiful coherence theorem tells us is monoidally equivalent to the free ribbon (n=C3=A9e tortile) category one = one object generator is marred and made less useful (certainly for application to knot theory and 3- and 4-manifold topology) by deciding one should work instead with a (2,infinity)-category with one object, framed point sets as 1-arrows, framed tangles as 2-arrows, isotopies as 3-arrows, isotopies of isotopies as 4-arrows, and so ad infinitum. Or, maybe not, but only if one has an application for which the (2,infinity)-category is the right level of weakness. Best Thoughts, David Yetter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]