From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3901 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: "prime" monads? Date: Thu, 13 Sep 2007 18:50:19 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019591 10783 80.91.229.2 (29 Apr 2009 15:39:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:51 +0000 (UTC) To: 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 1IWChE-0004q2-Ho for categories-list@mta.ca; Fri, 14 Sep 2007 12:03:04 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 25 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:3901 Archived-At: 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