From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7917 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: adjoints to lax-idempotent algebra structures Date: Fri, 15 Nov 2013 22:20:01 -0800 Message-ID: Reply-To: Michael Shulman NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1384695555 14420 80.91.229.3 (17 Nov 2013 13:39:15 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 17 Nov 2013 13:39:15 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Sun Nov 17 14:39:21 2013 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Vi2ZN-00064J-GX for gsmc-categories@m.gmane.org; Sun, 17 Nov 2013 14:39:21 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:38064) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1Vi2Xs-0003Xt-JD; Sun, 17 Nov 2013 09:37:48 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Vi2Xr-0007nE-4w for categories-list@mlist.mta.ca; Sun, 17 Nov 2013 09:37:47 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7917 Archived-At: Let T be a lax-idempotent (i.e. Kock-Zoberlein) 2-monad (or pseudomonad). Then to give a pseudo T-algebra structure on an object A is to give a left adjoint a : TA -> A to the unit e : A -> TA. Has anyone studied and/or named the class of T-algebras for which the algebra structure map admits a further left adjoint? In examples, this seems to be a sort of "super-exactness" condition. Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]