From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5011 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: monad: (k-Set \downarrow -): Set -->Set Date: Tue, 23 Jun 2009 11:27:17 +0100 (BST) Message-ID: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1245763792 25692 80.91.229.12 (23 Jun 2009 13:29:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 23 Jun 2009 13:29:52 +0000 (UTC) To: Peter Selinger , dspivak@uoregon.edu, categories@mta.ca Original-X-From: categories@mta.ca Tue Jun 23 15:29:50 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MJ64K-0003DB-Gd for gsmc-categories@m.gmane.org; Tue, 23 Jun 2009 15:29:48 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MJ5RU-0005t7-Om for categories-list@mta.ca; Tue, 23 Jun 2009 09:49:40 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5011 Archived-At: > In the case where k=omega, T is the well-known finite multiset monad, > which associates to each S the free commutative monoid generated by S > (whose elements are also known as finite multisets in S). > > For other k, I would call this the "monad of multisets of size less > than k". I think this works for any infinite small cardinal, not just > regular ones. You really do need the regularity. Otherwise removing brackets from a k-small multiset of k-small multisets might yield something bigger than a k-small multiset, and then one cannot define a multiplication for the monad. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]