From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5758 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: bilax monoidal functors Date: Fri, 7 May 2010 11:03:28 -0700 Message-ID: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1273276140 22631 80.91.229.12 (7 May 2010 23:49:00 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 7 May 2010 23:49:00 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Sat May 08 01:48:59 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 1OAXHu-00074h-5c for gsmc-categories@m.gmane.org; Sat, 08 May 2010 01:48:58 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OAWko-0001bn-JR for categories-list@mta.ca; Fri, 07 May 2010 20:14:46 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5758 Archived-At: Andr=C3=A9 Joyal wrote: > I wonder who first introduced the notion of bilax monoidal functor and > when? > I believe that Aguiar and Mahajan were the first to formally introduce this concept, though the Alexander-Whitney-Eilenberg-MacLane example has been around for a long time. On the n-Category Cafe, Kathryn Hess recently wrote: > The A-W/E-Z equivalences for the normalized chains functor are a special > case of the strong deformation retract of chain complexes that was > constructed by Eilenberg and MacLane in their 1954 Annals paper "On the > groups H(=CF=80,n). II". For any commutative ring R, they defined chain > equivalences between the tensor product of the normalized chains on two > simplicial R-modules and the normalized chains on their levelwise tensor > product. > > Steve Lack and I observed recently that the normalized chains functor is > actually even Frobenius monoidal. We then discovered that Aguiar and Maha= jan > already had a proof of this fact in their recent monograph. :-) > I forget if "Frobenius monoidal" is a precise synonym of "bilax monoidal". Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]