From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5766 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax monoidal functors Date: Sat, 8 May 2010 16:19:22 -0700 Message-ID: References: Reply-To: John Baez NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1273443059 27631 80.91.229.12 (9 May 2010 22:10:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 9 May 2010 22:10:59 +0000 (UTC) To: categories Original-X-From: categories@mta.ca Mon May 10 00:10:59 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 1OBEi9-0007pt-5D for gsmc-categories@m.gmane.org; Mon, 10 May 2010 00:10:57 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OBEEE-0000fp-5G for categories-list@mta.ca; Sun, 09 May 2010 18:40:02 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5766 Archived-At: John wrote: > I forget if "Frobenius monoidal" is a precise synonym of "bilax monoidal". > Steve replied: > No it's not. Frobenius monoidal is to Frobenius algebras as bilax monoidal > is to bialgebras. > > In particular a Frobenius monoidal functor 1-->C is a Frobenius algebra in > C; a bilax monoidal functor 1-->C is a bialgebra in C. > Okay, I should have guessed. So the normalized chains functor from simplicial abelian groups to chain complexes is both Frobenius monoidal and bilax monoidal? We were talking a while back about structures like the group algebra of a finite group, which is both a Frobenius algebra and a bialgebra. I guess that means every finite group gives a functor from the terminal category to Vect that's both Frobenius monoidal and bilax monoidal? Is there some slick way to understand why? Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]