From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1825 Path: news.gmane.org!not-for-mail From: Oswald Wyler Newsgroups: gmane.science.mathematics.categories Subject: Complete atomic Boolean algebra: Reference? Date: Sun, 4 Feb 2001 15:25:01 -0500 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018128 656 80.91.229.2 (29 Apr 2009 15:15:28 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:28 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Feb 4 18:59:30 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f14MH6S16280 for categories-list; Sun, 4 Feb 2001 18:17:06 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: owyler@localhost Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 18 Xref: news.gmane.org gmane.science.mathematics.categories:1825 Archived-At: Every reader of this post probably knows that the algebras for the monad on sets induced by the self-adjoint contravariant powerset functor are the complete atomic Boolean algebras, with maps preserving all infima and all suprema as morphisms. I know how to prove this without much trouble, but I have not been able to find a proof of this fact, or even a good reference to such a proof, in the literature available to me at my present location (which is essentially what I have at home). If you know such a reference, please e-mail it to me at owyler@nqi.net. Related question. The functor on sets which assigns to every set X the set of increasing subsets of PX is the functor part of a monad, with completely distributive complete lattices as algebras. Again, I have a proof but no references.