From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3815 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Maps of monads - references Date: Tue, 10 Jul 2007 17:54:35 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019540 10407 80.91.229.2 (29 Apr 2009 15:39:00 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:00 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jul 10 20:05:02 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jul 2007 20:05:02 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8Oh9-0001QH-Hk for categories-list@mta.ca; Tue, 10 Jul 2007 20:00:35 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 9 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:3815 Archived-At: I think that somewhere Harry Appelgate did something like that, probably in his Ph.D. thesis. Whether he ever published it, I cannot now say. Michael On Tue, 10 Jul 2007, 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 > > >