From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6027 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Tue, 3 Aug 2010 07:12:08 +1000 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: multipart/alternative; boundary=001636833d4a4efffe048cdda75a X-Trace: dough.gmane.org 1280788579 24425 80.91.229.12 (2 Aug 2010 22:36:19 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 2 Aug 2010 22:36:19 +0000 (UTC) Cc: Categories mailing list To: "Prof. Peter Johnstone" Original-X-From: majordomo@mlist.mta.ca Tue Aug 03 00:36:17 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Og3cD-0002zP-Bc for gsmc-categories@m.gmane.org; Tue, 03 Aug 2010 00:36:13 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50052) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Og3aq-0003Ce-Q3; Mon, 02 Aug 2010 19:34:48 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Og3al-0002eX-Jw for categories-list@mlist.mta.ca; Mon, 02 Aug 2010 19:34:43 -0300 In-Reply-To: Original-Content-Type: text/plain; charset=ISO-8859-1 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6027 Archived-At: Ah, good, thanks. Which suggests that for idempotent monads, tensor = sum might not be so stupid after all. On 3 August 2010 00:17, Prof. Peter Johnstone wrote: > Dear Richard, > > Your (*) is not an additional condition. Being a sheaf for both J and J' > is equivalent to being a sheaf for their join (which I presume is what you > mean by J n J'). For a proof, see A4.5.16 in the Elephant. > > Peter > --------------------------- > > On Sun, 1 Aug 2010, Richard Garner wrote: > > Further to my earlier question: >> >> -- Given idempotent monads S, T on a category C for which we can speak of >> >>> the tensor of S and T, is it always the case that S * T is isomorphic to >>> S + >>> T? >>> ,,, [For admin and other information see: http://www.mta.ca/~cat-dist/ ]