From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6033 Path: news.gmane.org!not-for-mail From: Sergey Goncharov Newsgroups: gmane.science.mathematics.categories Subject: Re: Tensor of monads Date: Thu, 05 Aug 2010 22:06:21 +0200 Message-ID: References: Reply-To: Sergey Goncharov 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 1281139630 26099 80.91.229.12 (7 Aug 2010 00:07:10 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 7 Aug 2010 00:07:10 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Aug 07 02:07:08 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 1OhWwM-0000dt-0x for gsmc-categories@m.gmane.org; Sat, 07 Aug 2010 02:07:06 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50236) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OhWtj-0007eG-7Z; Fri, 06 Aug 2010 21:04:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OhWte-0004Gy-6Y for categories-list@mlist.mta.ca; Fri, 06 Aug 2010 21:04:18 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6033 Archived-At: Thank you Peter and Andr=E9 and all the participants of the discussion. It is indeed very helpful. Richard Garner wrote: > On the other hand, Andr=E9's example raises a question which I find qui= te > interesting. Andr=E9 describes two reflective subcategories of the orde= red > class of ordinal numbers, and then says that, their intersection being > empty, the tensor of the corresponding idempotent monads cannot exist. = I > would be inclined to say that this shows that the coproduct of these mo= nads > does not exist I guess it applies both to the tensor and to the sum as well as to any=20 other case where we need to form a span of monad morphism: S -> R <- T=20 and which precisely can not be formed in this case. It looks like there are two counterexamples, both of which are based on=20 the construction of tricky underlying categories. But what about=20 existence of the tensor over Sets? I guess this is still open. I tried=20 to think about the tensor product of a continuation monad with itself as=20 a possible counterexample, without any success though. Usually,=20 continuation monad performs well when it comes to constructing=20 counterexamples but it is difficult to see what the tensor product of it=20 with itself is supposed to look like. Thanks again, Sergey. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]