From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5774 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors?= Date: Mon, 10 May 2010 11:58:46 -0300 Message-ID: References: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1273539873 18097 80.91.229.12 (11 May 2010 01:04:33 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 11 May 2010 01:04:33 +0000 (UTC) To: Andre Joyal Original-X-From: categories@mta.ca Tue May 11 03:04:31 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 1OBdte-0001EL-KF for gsmc-categories@m.gmane.org; Tue, 11 May 2010 03:04:30 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBdDG-0002Md-Eh for categories-list@mta.ca; Mon, 10 May 2010 21:20:42 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5774 Archived-At: Andre points out: "To call a monoidal category 1-braided is kind of confusing because there is no commutation structure on a general monoidal category. A monoidal category is 0-braided." Being an outsider, with no previous neither usage or opinion on this=20 terminology beyond just monoidal and/or tensor category, this seems to=20 me definitive, and more than enough to settle the question. e.d. Andre Joyal wrote: > Dear John and Michael, >=20 > 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 >=20 > http://en.wikipedia.org/wiki/Storey#Numbering >=20 > 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 >=20 > More seriously, John wrote: >=20 >> I use "k-tuply monoidal" to mean what you'd call "(k-1)-braided". Thi= s >> seems preferable to me, not because it sounds nicer - it doesn't - but >> because it starts counting at a somewhat more natural place. I believ= e that >> counting monoidal structures is more natural than counting braidings. >=20 > Michael wrote: >=20 >> I am using a mixture of your terminologies: >> monoidal =3D 1-braided >> braided =3D 2-braided >> sylleptic =3D 3-braided >=20 > I understand your ideas both. Along the same line we could also use: >=20 > E1-category =3D Monoidal =20 > E2-category =3D Braided monoidal=20 > E3-category =3D ..... > ..... >=20 > John wrote: >=20 >> By the way: I don't remember anyone on this mailing list ever asking i= f >> their own terminology is good. I only remember them complaining about= other >> people's terminology. I applaud your departure from this unpleasant >> tradition! >=20 > 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. >=20 > I do think that my terminology for higher braided > monoidal categories is quite good. > Let me say a few things in its defense: >=20 > 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 >=20 >=20 > I wonder who introduced the notion of E(n)-space and > the terminology? >=20 >=20 > Best regards,=20 > Andr=E9 >=20 >=20 >=20 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]