From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7239 Path: news.gmane.org!not-for-mail From: "Francisco Marmolejo (314)" Newsgroups: gmane.science.mathematics.categories Subject: Re: 2-categorical monad functor lifting Date: Mon, 26 Mar 2012 10:05:45 -0600 (CST) Message-ID: References: Reply-To: "Francisco Marmolejo (314)" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=UTF-8 Content-Transfer-Encoding: QUOTED-PRINTABLE X-Trace: dough.gmane.org 1332861063 15668 80.91.229.3 (27 Mar 2012 15:11:03 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 27 Mar 2012 15:11:03 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue Mar 27 17:11:02 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 1SCY34-0004YD-3K for gsmc-categories@m.gmane.org; Tue, 27 Mar 2012 17:11:02 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45441) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1SCY1a-0005Fi-3X; Tue, 27 Mar 2012 12:09:30 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1SCY1Y-0006ic-FI for categories-list@mlist.mta.ca; Tue, 27 Mar 2012 12:09:28 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7239 Archived-At: Dear Steve, you may want to check Coherence for pseudodistributive laws revisited F. Marmolejo and R.J. Wood Theory and Applications of Categories, Vol. 20, No. 6, 2008, pp. 74=E2=80= =9384. and the bibliography there-in for the pseudo case (and for pseudomonads).= =20 The standard reference for the 1-categorical case must surely be The formal theory of monads R. Street J. Pure Appl. Algebra 2 (1972) F. Marmolejo On Mon, 26 Mar 2012, Steve Vickers wrote: > 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/ ] > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]