From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3899 Path: news.gmane.org!not-for-mail From: "Greg Meredith" Newsgroups: gmane.science.mathematics.categories Subject: Re: "prime" monads? Date: Thu, 13 Sep 2007 16:06:30 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019590 10777 80.91.229.2 (29 Apr 2009 15:39:50 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:50 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Sep 14 12:11:46 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 14 Sep 2007 12:11:46 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IWCjO-00058S-1K for categories-list@mta.ca; Fri, 14 Sep 2007 12:05:18 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:3899 Archived-At: Fred, Thanks. My 'intuition' is that there are some adjoint decompositions that genuinely reveal internal structure of the monad and others that ... make no such disclosure ;-). But, perhaps i can disabuse myself of this with some application to calculation. Best wishes, --greg On 9/13/07, Fred E.J. Linton wrote: > > Greg Meredith asks, > > > ... are there monads such that the only adjoint > > situations giving rise to them are the Kleisli and Eilenberg-Moore > algebras? > > NOt even the identity monad on SETS has this property, as it is > the adjunction monad also for the adjoint pair > > [underlying pointset]: [topological spaces] --> SETS , > [discrete topology on]: SETS --> [topological spaces] . > > There ARE a few monads for which the Kleisli and E-M categories > "coincide," however, beyond the identity monads. First example > coming to mind is the FreeVectorSpace monad on SETS. I'm sure > other Categories-readers will point out more. > > -- Fred