From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2268 Path: news.gmane.org!not-for-mail From: Oswald Wyler Newsgroups: gmane.science.mathematics.categories Subject: Query Date: Mon, 5 May 2003 13:46:43 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018537 3326 80.91.229.2 (29 Apr 2009 15:22:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed May 7 14:24:53 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 May 2003 14:24:53 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DSed-0000GH-00 for categories-list@mta.ca; Wed, 07 May 2003 14:24:31 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 3 Original-Lines: 12 Xref: news.gmane.org gmane.science.mathematics.categories:2268 Archived-At: For every set Z, there is a self-adjoint contravariant functor Q=ENS(--,Z), with unit/counit h:Id-->Q^op Q given by (h_X)(x)(f)=f(x). Let Q-alg denote the category of algebras for the monad induced by this self-adjunction. If Z is not empty or a singleton, then the comparison functor ENS^op-->Q-alg is an equivalence by results of M. Sobral. If Z has two members, then Q-alg is isomorphic to CaBool, the category of complete atomic Boolean algebras. What is known about Q-alg if Z has more than two members (beyond the fact that Q-alg and CaBool are equivalent)?