From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5779 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors Date: Mon, 10 May 2010 23:17:15 -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 1273625354 15445 80.91.229.12 (12 May 2010 00:49:14 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 12 May 2010 00:49:14 +0000 (UTC) To: "Urs Schreiber" , Original-X-From: categories@mta.ca Wed May 12 02:49:13 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 1OC08M-0000uN-OR for gsmc-categories@m.gmane.org; Wed, 12 May 2010 02:49:10 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBzfG-0007TL-5z for categories-list@mta.ca; Tue, 11 May 2010 21:19:06 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5779 Archived-At: Dear Urs and John, I see no real conflict between your terminology and mine. I do use the notion of n-fold monoid in my work, for example in my "Notes on Quasi-categories". An *algebraic theory* is defined to be a (quasi-)category with finite = products. The n-fold tensor power of the theory of monoids M is the theory of n-fold monoids =3D E(n)-monoids for every n. I am sketching a proof of the Stabilisation Hypothesis at section 43.5 = of my notes. The hypothesis is formulated in terms of an equivalence of theories:=20 . It follows that the quasi-category of (n+2)-fold monoidal n-categories=20 is equivalent to the quasi-category of symmetric monoidal n-categories. Best,=20 Andr=E9 -------- Message d'origine-------- De: categories@mta.ca de la part de Urs Schreiber Date: lun. 10/05/2010 06:28 =C0: John Baez Objet : categories: Re: bilax monoidal functors =20 > An n-tuply monoidal k-category is (conjecturally) a special sort of > (n+k)-category By the way, some progress on this is available from John Francis' and Jacob Lurie's discussion of k-tuply monoidal (n,1)-categories as those equipped with a little k-cubes action. In particular there is a proof of the stabilization hypothesis for (n,1)-categories this way, and an analog of the May recognition theorem for parameterized oo-groupoids, i.e. (oo,1)-sheaves. Some of this is summarized with pointers to references here: http://ncatlab.org/nlab/show/k-tuply+monoidal+n-category Best, Urs [For admin and other information see: http://www.mta.ca/~cat-dist/ ]