From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2703 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: comparing cotriples via an adjoint pair Date: Fri, 21 May 2004 21:54:06 +0100 (BST) 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 1241018839 5391 80.91.229.2 (29 Apr 2009 15:27:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:27:19 +0000 (UTC) To: categories@mta.ca 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 1BS015-0005Jh-00 for categories-list@mta.ca; Sun, 23 May 2004 17:56:19 -0300 In-Reply-To: <5.1.0.14.2.20040520232118.0235f070@mailbox.syr.edu> X-DPMMS-Scan-Signature: 52b2ec4a892cc9295ce0dcc23e061bcd Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 25 Original-Lines: 29 Xref: news.gmane.org gmane.science.mathematics.categories:2703 Archived-At: 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 > See (for the dual situation) an old paper of mine: Adjoint lifting theorems for categories of algebras, Bull London Math. Soc. 7 (1975), 294--297. I should say (before others say it for me) that this was not the first place the result appeared: it (and much more) was in the famous unpublished (and largely unwritten) thesis of Bill Butler. But Gaunce asked for a published reference. Peter Johnstone