From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6022 Path: news.gmane.org!not-for-mail From: Ronnie Brown Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Mon, 02 Aug 2010 10:47:12 +0100 Message-ID: References: <4C5224A4.4000105@informatik.uni-bremen.de> Reply-To: Ronnie Brown NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1280752468 7235 80.91.229.12 (2 Aug 2010 12:34:28 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 Aug 2010 12:34:28 +0000 (UTC) Cc: categories@mta.ca To: Tom Leinster Original-X-From: majordomo@mlist.mta.ca Mon Aug 02 14:34:26 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OfuDq-00010m-33 for gsmc-categories@m.gmane.org; Mon, 02 Aug 2010 14:34:26 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53290) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OfuBy-0000Ei-VG; Mon, 02 Aug 2010 09:32:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OfuBw-0006p0-SA for categories-list@mlist.mta.ca; Mon, 02 Aug 2010 09:32:28 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6022 Archived-At: There is another possibly relevant area. It used to be standard (e.g.=20 Huppert, Endliche Gruppen) that the only tensor product of groups was=20 the usual tensor product of their abelianisations. This is because if=20 b:G \times G \to H is a bimorphism then by expanding b(gg',hh') in two ways, and applying cancellation, you get a=20 commutativity condition. However with Jean-Louis Loday we realised, as=20 others had before us, that another interesting condition is for b to be=20 a biderivation, since this is one of the rules satisfied by the=20 commutator map [ , ] : G \times G \to G. The universal object for=20 biderivations is then the nonabelian tensor square G \otimes G. This=20 idea applies to other areas such as Lie algebras. A bibliography of 100=20 items is on www.bangor.ac.uk/r.brown/nonabtens.html Any possibility for monads?? This may be wild, but on the other hand.....= ... On another tack, my memory is, and this puzzled me at first, that the=20 paper Loday, Jean-Louis=20 $K$-th=E9orie alg=E9brique et repr=E9sentations de groupes. *(French)* /Ann. Sci. =C9cole Norm. Sup. (4)/=20 =20 * 9 * (1976), no. 3, 309--377. uses a multiplication induced essentially by a structure of a monoid=20 with a compatible structure of semigroup; so the Eckmann-Hilton argument=20 does not apply! Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]