From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6349 Path: news.gmane.org!not-for-mail From: Todd Trimble Newsgroups: gmane.science.mathematics.categories Subject: Re: Communes paper, schismatic objects Date: Mon, 01 Nov 2010 19:52:59 -0400 Message-ID: Reply-To: Todd Trimble NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=Windows-1252; reply-type=response Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1288739764 20491 80.91.229.12 (2 Nov 2010 23:16:04 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 2 Nov 2010 23:16:04 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Wed Nov 03 00:15:59 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PDQ57-0002YQ-VG for gsmc-categories@m.gmane.org; Wed, 03 Nov 2010 00:15:58 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:34166) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PDQ48-0004TY-7X; Tue, 02 Nov 2010 20:14:56 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PDQ41-00025x-Cs for categories-list@mlist.mta.ca; Tue, 02 Nov 2010 20:14:49 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6349 Archived-At: A couple of things related to recent comments on "schizophrenic". Vaughan Pratt wrote, with regard to possible alternatives to "schizophren= ic" "So I followed Tom's pointer http://ncatlab.org/nlab/show/dualizing+object linking to a discussion of alternatives, which seemed inconclusive. Sam (Staton?) made the point however that even if schizophrenia is not the appropriate word, schizo is the appropriate prefix, having derived from the Greek 'split'. " Although the discussion at the nLab might appear inconclusive, in actual fact a number of people at the nLab and n-Category Cafe seem to have provisionally adopted "ambimorphic", which I coined with the intended meaning, "having both forms". I actually feel that is very appropriate in practice; for example, in classical Stone duality, it is not enough to sa= y=20 the dualizing object 2 is "split" between being seen as a compact Hausdorff space and as a Boolean algebra. It is both at once: a Boolean algebra object in the category of compact Hausdorff spaces, and we need both forms in the same body so that we can say hom_{CH}(-, 2) is a Boolean algebra valued functor. With regard to Dusko's recent comments: it's quite understandable that "political correctness" and endless debates over terminology can become tiresome. But I'm not sure "political correctness" is quite the angle fro= m which Tom's objection comes. At the Cafe he brought it up here: http://golem.ph.utexas.edu/category/2007/01/more_on_duality.html#c007089 (where you can also see the consequent discussion of suggested alternativ= es) and the sense I get is that it's not so much about "protecting the weak" as it is about wishing not to perpetuate pop misconceptions. But putting all that aside, perhaps the emphasis on being "split" is not quite accura= te in the first place, or at least should be reconsidered, as I argue above. Todd ----- Original Message -----=20 From: "Vaughan Pratt" To: "categories list" Sent: Monday, November 01, 2010 1:44 PM Subject: categories: Communes paper, schismatic objects A couple of things. First, I neglected to mention that "Communes via Yoneda, from an Elementary Perspective," Fundamenta Informaticae 123 (2010) 1=9616, DOI 10.3233/FI-2010-315 is about to appear and won't be findable by Google just yet. Those interested in seeing it sooner can find it on my site at http://boole.stanford.edu/pub/CommunesFundInf2010.pdf Second, as I said I wasn't passing judgment on the wisdom of avoiding the term "schzophrenic" but merely pointing out the associated cost, which needs to be balanced against the harm of any given word. So I followed Tom's pointer http://ncatlab.org/nlab/show/dualizing+object linking to a discussion of alternatives, which seemed inconclusive. Sam (Staton?) made the point however that even if schizophrenia is not the appropriate word, schizo is the appropriate prefix, having derived from the Greek "split." So it is the medical condition that is inappropriately named, namely as "split madness," with phrenitis and frenzy having a common origin. With that in mind it occurred to me that "schismatic" might be a suitable alternative, as providing better continuity with the older terminology by coming from the same root schizo, but more honestly so than schizophrenia since in this case there really is a multiple personality, and moreover there's nothing insane about it. (And it's a syllable shorter to boot.) Third, while it is true that the schismatic object (to give the term a trial run) is usually observed manifesting its split personality in different categories, this is not the case in *-autonomous categories where I and _|_ are the Jekyll and Hyde of the same category. (I apologize to readers of this list with either of those surnames.) In all the examples I'm aware of, the two categories in which the schismatic object occurs (once in each) admit a common completion to a *-autonomous category which embeds one object as I and the other as _|_. Considering them to be the "same" object found in two categories misses the contravariance between them, which is brought out more clearly by this joint completion, where they are clearly not the same object but a pair of dual objects. My paper accounts for C.I. Lewis's qualia by viewing them as morphisms running from I to _|_. If I and _|_ are rigid (|C(x,x)|=3D1) as for Chu(Set,K)), the presence of a morphism from _|_ to I is inconsistent in the sense that it collapses Hom(I,_|_) to a singleton, since I and _|_ respectively generate and cogenerate. So in order to have more than one quale (in the Chu setting) there cannot be any morphism from _|_ to I. (That was mainly in the nature of background on the neighborhood of I and _|_.) Vaughan [For admin and other information see: http://www.mta.ca/~cat-dist/ ]