From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7238 Path: news.gmane.org!not-for-mail From: Steve Vickers Newsgroups: gmane.science.mathematics.categories Subject: 2-categorical monad functor lifting Date: Mon, 26 Mar 2012 10:23:33 +0100 Message-ID: Reply-To: Steve Vickers NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1332762722 2787 80.91.229.3 (26 Mar 2012 11:52:02 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 26 Mar 2012 11:52:02 +0000 (UTC) Cc: Bertfried Fauser To: Categories Original-X-From: majordomo@mlist.mta.ca Mon Mar 26 13:52:00 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1SC8So-0007gw-Sl for gsmc-categories@m.gmane.org; Mon, 26 Mar 2012 13:51:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43531) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SC8RX-0002qf-Q8; Mon, 26 Mar 2012 08:50:35 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SC8RW-0007tX-8Y for categories-list@mlist.mta.ca; Mon, 26 Mar 2012 08:50:34 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7238 Archived-At: As we know, a monad functor between two monads (possibly on different categories) can be lifted to a functor between the algebra categories. Fauser and I needed a corresponding 2-categorical result: a 2-monad 2-functor (of course, the natural transformation involved needs to be 2-natural) between two 2-monads (possibly on different 2-categories) can be lifted to a 2-functor between the lax algebra 2-categories. Also the lifting preserves pseudo-ness and strictness of the algebras. We checked all the equations and it works, but we're not experts on the 2-categorical literature and we wonder if it's already known. Our first literature searches haven't shown up anything - though even the 1-categorical case (which surely is well known) is elusive. Has anyone seen this result before? Steve Vickers. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]