From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3169 Path: news.gmane.org!not-for-mail From: "Reinhard Boerger" Newsgroups: gmane.science.mathematics.categories Subject: Re: Monads on finite categories Date: Mon, 27 Mar 2006 10:06:02 +0200 Organization: FernUniversitaet Message-ID: <4427B908.13265.48C862@reinhard.boerger.fernuni-hagen.de> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7BIT X-Trace: ger.gmane.org 1241019133 7544 80.91.229.2 (29 Apr 2009 15:32:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:13 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Mar 28 19:01:40 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 28 Mar 2006 19:01:40 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FON21-0005iw-Dy for categories-list@mta.ca; Tue, 28 Mar 2006 18:51:21 -0400 Content-description: Mail message body X-prewhitelist: your reply will pass through without greylisting Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 115 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:3169 Archived-At: Hello, Tom Leinster wrote: > 1. Are there significant or interesting examples of monads on finite > categories? I want to look beyond monads on posets, a.k.a. closure > operators. (Since a finite category with binary sums or products > is necessarily a poset, some of the usual examples of monads reduce > to this case.) I can only think of one class of examples > (described below), and I don't know if it's particularly > significant. Idempotent monads correspond to full reflective subcategories; so the only examples are induced by full reflective subcategories of finite categories. Greetings Reinhard