From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5808 Path: news.gmane.org!not-for-mail From: Jeff Egger Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors Date: Sat, 15 May 2010 09:54:21 -0700 (PDT) Message-ID: References: Reply-To: Jeff Egger 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 1274023928 18815 80.91.229.12 (16 May 2010 15:32:08 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 16 May 2010 15:32:08 +0000 (UTC) To: John Baez , categories , Original-X-From: categories@mta.ca Sun May 16 17:32:06 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 1ODfp0-0008Bp-DA for gsmc-categories@m.gmane.org; Sun, 16 May 2010 17:32:06 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ODfO3-0006cj-EC for categories-list@mta.ca; Sun, 16 May 2010 12:04:15 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5808 Archived-At: >> But I think "braided =3D doubly monoidal" is even=0A> > better.=A0 Afte= r all, a=0A> > monoidal category has one tensor product; a braided=0A> > mo= noidal category has=0A> > two compatible tensor products, and a symmetric= =0A> > monoidal category has three.=0A> =0A> The trouble is that n-monoidal= categories already exist.=0A> They were=0A> introduced my Balteanu, Fioder= owicz, Shwantzl and Vogt.=0A> This is why I=0A> also see n-tuply monoidal a= s confusing. I do not say that=0A> they sound=0A> identical but certainly v= ery close to each other.=0A=0AThis is a strong point. Obviously n-tuply mo= noidal category=0Ashould mean category with n "compatible" monoidal structu= res;=0Abut there many possible meanings of "compatible". One choice =0Alea= ds to a single monoidal structure with an (n-1)-braiding;=0Abut a different= choice leads to the notion of BFSV. In fact,=0AI think that even the BFSV= notion is too strict---it forces =0Aall the units to be the same, where I = think one should allow=0Athem to be different (in general). That is, I thi= nk it would=0Abe reasonable to use "doubly monoidal category" to mean =0A(p= seudo)monoid internal to LAX (rather than STRONG, or even =0ANORMAL). =0A= =0ACheers,=0AJeff.=0A=0A=0A [For admin and other information see: http://www.mta.ca/~cat-dist/ ]