From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3834 Path: news.gmane.org!not-for-mail From: Prof. Dr. Pumpluen Newsgroups: gmane.science.mathematics.categories Subject: Re: Maps of monads - references Date: Sun, 22 Jul 2007 11:14:07 +0200 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 1241019551 10516 80.91.229.2 (29 Apr 2009 15:39:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:11 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Sun Jul 22 11:39:53 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 22 Jul 2007 11:39:53 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ICcSc-0006dv-EJ for categories-list@mta.ca; Sun, 22 Jul 2007 11:31:02 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 28 Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:3834 Archived-At: There is still another, very detailed reference (probably earlier) to this topic in my paper "Eine Bemerkung ueber Monaden und adjungierte Funktoren", Math. Ann.185, 329-337 (1970). Best regards Nico Pumpluen. On Jul 10, 2007, at 9:25 AM, Steven R. Costenoble wrote: > In Toposes, Triples, and Theories, Barr and Wells define a morphism > of triples (which, being a student of Peter May, I will call a map of > monads) in the context of two monads on a given category C. I have a > situation where I have two categories C and D, a monad S on C, a > monad T on D, and a functor F: C -> D. There is a fairly obvious > generalization of the TTT definition, to say that a map from S to T > is a natural transformation FS -> TF making certain diagrams commute. > My guess is that someone else noticed this long ago, so I'm looking > for references to where this has appeared in the literature. I'm > particularly interested in references that include the fact (at > least, I'm pretty sure it's a fact) that such maps are in one-to-one > correspondence with extensions of F to a functor between the > respective Kleisli categories of S and T. > > Thanks in advance. > > --Steve Costenoble > > >