From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5297 Path: news.gmane.org!not-for-mail From: burroni@math.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: question on pseudomorphisms Date: Mon, 23 Nov 2009 13:55:01 +0100 Message-ID: Reply-To: burroni@math.jussieu.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=ISO-8859-1;DelSp="Yes";format="flowed" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1259023247 22356 80.91.229.12 (24 Nov 2009 00:40:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 24 Nov 2009 00:40:47 +0000 (UTC) To: Categories mailing list Original-X-From: categories@mta.ca Tue Nov 24 01:40:40 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from [138.73.1.1] (helo=mailserv.mta.ca) by lo.gmane.org with esmtp (Exim 4.50) id 1NCjSR-0005NT-7v for gsmc-categories@m.gmane.org; Tue, 24 Nov 2009 01:40:39 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NCj0V-0002dt-8I for categories-list@mta.ca; Mon, 23 Nov 2009 20:11:47 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5297 Archived-At: Dear all, Has the following question been already studied and, if it is the case =20 (it is my opinion), where ? Let T be a monad on Cat (not necessarily a 2-monad), C the category of =20 T-algebras and C' the cat=E9gorie with the same objets but with =20 pseudomorphisms (morphisms up to natural isomorphisms --- eventually =20 with coherences). The inclusion i : C --> C' has a left adjoint j : C' --> C. The question is : for all T-algebra A, is the canonical morphisms m : =20 A --> i(j(A)) an equivalence (of the underlying categories) ? Regards, Albert [For admin and other information see: http://www.mta.ca/~cat-dist/ ]