From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5769 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors?= Date: Sun, 9 May 2010 12:26:02 -0400 Message-ID: References: Reply-To: Andre Joyal 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 1273443275 28153 80.91.229.12 (9 May 2010 22:14:35 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 9 May 2010 22:14:35 +0000 (UTC) To: "John Baez" , "categories" Original-X-From: categories@mta.ca Mon May 10 00:14:34 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 1OBEle-0000H8-0v for gsmc-categories@m.gmane.org; Mon, 10 May 2010 00:14:34 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBEI2-0000mS-7K for categories-list@mta.ca; Sun, 09 May 2010 18:43:58 -0300 Thread-Topic: RE : categories: bilax monoidal functors Thread-Index: AcrvAhLxQy5ui2NfR/WSfT+ighemCQAfHG46 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5769 Archived-At: Dear John and Michael, It all depends on where you start counting. For americans, the first floor of a buiding is the ground floor but for most europeans, it is the floor right above:=20 http://en.wikipedia.org/wiki/Storey#Numbering We sometime need to recall in which part of the world we are=20 when we take an elevator! But a ten stories building is the same for everyone. =20 More seriously, John wrote: >I use "k-tuply monoidal" to mean what you'd call "(k-1)-braided". This >seems preferable to me, not because it sounds nicer - it doesn't - but >because it starts counting at a somewhat more natural place. I believe = that >counting monoidal structures is more natural than counting braidings. Michael wrote: >I am using a mixture of your terminologies: > monoidal =3D 1-braided > braided =3D 2-braided > sylleptic =3D 3-braided I understand your ideas both. Along the same line we could also use: E1-category =3D Monoidal =20 E2-category =3D Braided monoidal=20 E3-category =3D ..... ..... John wrote: >By the way: I don't remember anyone on this mailing list ever asking if >their own terminology is good. I only remember them complaining about = other >people's terminology. I applaud your departure from this unpleasant >tradition! My goal is to have a public discussion on terminology. 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. There is also a psychological aspect because a terminology looks natural if you use it long enough (it is a matter of a few days). I hope that a public discussion can help peoples=20 choosing their terminology. I do think that my terminology for higher braided monoidal categories is quite good. Let me say a few things in its defense: First, it extends naturally a terminology which is used=20 by the mathematical community since many decades. Only a specialist can truly appreciate E(k)-categories or=20 k-tuply monoidal categories. Second, a braiding is a commutation=20 structure. To call a monoidal category 1-braided is kind of=20 confusing because there is no commutation structure=20 on a general monoidal category. A monoidal category is 0-braided.=20 Third, a n-braided (topological or simplicial) group is exactly what=20 you need to describe the homotopy type of an n-connected space (n\geq = 1).=20 I wonder who introduced the notion of E(n)-space and the terminology? Best regards,=20 Andr=E9 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]