From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5760 Path: news.gmane.org!not-for-mail From: Andre Joyal Newsgroups: gmane.science.mathematics.categories Subject: Re: Q about_monoidal_functors? Date: Fri, 7 May 2010 22:59:41 -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 1273359417 23167 80.91.229.12 (8 May 2010 22:56:57 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 8 May 2010 22:56:57 +0000 (UTC) To: "Toby Bartels" , "categories" Original-X-From: categories@mta.ca Sun May 09 00:56:56 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 1OAsx1-0003qg-36 for gsmc-categories@m.gmane.org; Sun, 09 May 2010 00:56:51 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OAsRA-0001ZG-Ht for categories-list@mta.ca; Sat, 08 May 2010 19:23:56 -0300 Thread-Topic: categories: Re: Q. about monoidal functors Thread-Index: AcruP3RvAOJy4qrFSECGPKCum6kT2gAGwym+ Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5760 Archived-At: Dear Toby, Looping and delooping operations can be applied to spaces and to maps between spaces.=20 We should use a similar terminology for spaces and maps. For example: E-n space <--> E-n map Also for (higher) categories and functors.=20 monoidal category <---> monoidal functor braided monoidal category <----> braided monoidal functor 2-braided monoidal category <--> 2-braided monoidal functor 3-braided monoidal category <--> 3-braided monoidal functor ...... ...... ...... symmetric monoidal category <--> symmetric monoidal functor A (n+1)-braided monoidal n-category is symmetric by=20 the stabilisation hypothesis.=20 I believe that a (n+1)-braided monoidal functor=20 between (n+1)-braided monoidal n-categories is symmetric.=20 Is this part of the official stabilisation hypothesis? Best, Andr=E9=20 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]