From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3818 Path: news.gmane.org!not-for-mail From: "Steven R. Costenoble" Newsgroups: gmane.science.mathematics.categories Subject: Re: Maps of monads - references Date: Wed, 11 Jul 2007 09:04:47 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v752.3) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019542 10431 80.91.229.2 (29 Apr 2009 15:39:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:02 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Jul 11 15:19:51 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 11 Jul 2007 15:19:51 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1I8gbh-0006e5-IE for categories-list@mta.ca; Wed, 11 Jul 2007 15:08:09 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 12 Original-Lines: 34 Xref: news.gmane.org gmane.science.mathematics.categories:3818 Archived-At: Thanks, all, for the many replies (private as well as to the list). Among other interesting references, almost everyone suggested Ross Street's "The formal theory of monads" as well as the recent followup by Street and Steve Lack, "The formal theory of monads II." I'll add those to my summer reading list. --Steve Costenoble 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 > > >