From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5778 Path: news.gmane.org!not-for-mail From: Jeff Egger Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors Date: Mon, 10 May 2010 12:28:02 -0700 (PDT) Message-ID: References: Reply-To: Jeff Egger NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1273539921 18221 80.91.229.12 (11 May 2010 01:05:21 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 11 May 2010 01:05:21 +0000 (UTC) To: John Baez , categories , Original-X-From: categories@mta.ca Tue May 11 03:05:18 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OBduN-0001Qu-3m for gsmc-categories@m.gmane.org; Tue, 11 May 2010 03:05:15 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBdIR-0002Y9-9K for categories-list@mta.ca; Mon, 10 May 2010 21:26:03 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5778 Archived-At: Dear Andre, > My goal is to have a public discussion on terminology. It is good that you provoke us into having such discussions! > It can be very difficult to agree upon because > adopting one is like commiting to a rule of law, > to a moral code, possibly to a social code. > There is an emotional and social aspect to this > commitment. I don't understand this at all. A co-author of mine recently commented (complained?) that I seem to "change [my] notation as often as [my] underwear"; and I am not that much better with terminology. Indeed, I am overtly anarchist in this respect, and instinctively resist all attempts at codifying language. Most people would agree that the most important concepts deserve the shortest names; but people frequently (honestly) disagree over which concept is the most important. More significantly, attitudes often change with time! It is frustrating, then, that people will cling to archaic terminology for the sake of an emotional and social commitment. [A wonderful counter-example to this phenomenon is when Mike Barr gave his opinion that the meaning of star- autonomous category, which initially included symmetry, should not do so. I should also say that I think young mathematicians are generally worse at this than older ones. Indeed, the most extreme version of (what I perceive to be) the same phenomenon is that of the undergrad who cannot differentiate z=t^2 "because there is no x".] My objection to the phrase "autonomous category" (which Dusko brought up) has less to do with defending Fred Linton's original usage of that phrase than the fact that "autonomous category" is a special case (and, from one point of view, a rather uninteresting special case) of "star-autonomous category", whereas it sounds like "star-autonomous category" should mean an "autonomous category" with some extra structure. (And, of course, this once was the case, w.r.t. the older terminology.) This is confusing; hence one term or the other should be changed. I am, in fact, open to all suggestions, though I cannot help but prefer that "star-autonomous" be kept and "autonomous" changed. Cheers, Jeff. P.S. A propos of your first email in this thread, why bother with all those "lax"s? If you used > 1) strong monoidal > 2) monoidal > 3) comonoidal > 4) bimonoidal instead, then you would have > A monoid is a monoidal functor 1-->C, > a comonoid is a comonoidal functor 1-->C > and a bimonoid is a bimonoidal functor 1-->C. and you could even substitute > 5) ambimonoidal for "Frobenius", since "ambialgebra" has been used for "Frobenius algebra". Dare I point out that a strong monoidal functor 1-->C is a _trivial_ monoid? ;) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]