From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2701 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: comparing cotriples via an adjoint pair Date: Fri, 21 May 2004 16:30:36 -0400 (EDT) Message-ID: References: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018837 5381 80.91.229.2 (29 Apr 2009 15:27:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:17 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Sun May 23 18:00:11 2004 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 23 May 2004 18:00:11 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1BRzzv-0005HF-00 for categories-list@mta.ca; Sun, 23 May 2004 17:55:07 -0300 In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 23 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:2701 Archived-At: Although I cannot be sure, this looks an awful lot like an adjoint triple. I think Charles and I had a section of TTT on this. It was certainly not new with us and may have even been in Harry Appelgate's thesis back around 40 years ago. Michael On Thu, 20 May 2004, Gaunce Lewis wrote: > I have encountered a situation in which I have two categories C, D which > are related by a pair of adjoint functors L from C to D and R from D to > C. Also, there is a cotriple S on C and a cotriple T on D. Finally, there > is a natural isomorphism f from RT to SR. It seems that if a couple of > diagrams relating f to the structure maps of the cotriples commute, then > there is an induced adjoint pair relating the two coalgebra categories. Is > this, or something similar to it, in the literature in some easily > referenced place? > > Thanks, > Gaunce > > > >