From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5012 Path: news.gmane.org!not-for-mail From: Mark.Weber@pps.jussieu.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: monad: (k-Set \downarrow -): Set -->Set Date: Tue, 23 Jun 2009 06:43:55 +0200 (CEST) Message-ID: Reply-To: Mark.Weber@pps.jussieu.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=iso-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1245763797 25711 80.91.229.12 (23 Jun 2009 13:29:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 23 Jun 2009 13:29:57 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Tue Jun 23 15:29:55 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 1MJ64P-0003H7-Es for gsmc-categories@m.gmane.org; Tue, 23 Jun 2009 15:29:53 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MJ5No-0005Yp-KJ for categories-list@mta.ca; Tue, 23 Jun 2009 09:45:52 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5012 Archived-At: Peter Johnstone is right -- the monad David described doesn't exist, thus neither does the monad morphism I described in my other post (... sorry!)= . Perhaps the fibrations monad is still of interest. One could fix a skeleton of Set_k, and for k =3D cardinality of natural numbers this works fine, and the monad on Set you get is the monoid monad= . However for bigger k you're likely to run into problems when trying to do this sort of thing. However it isn't true that the monad >> (... on Cat, where we replace k-Set with k-Cat.) is the k-coproduct completion monad -- you need to keep k-Set but work in Cat and take lax slices, ie take the monad on Cat which has underlying endofunctor X |-> k-Set // X (where // means "lax slice") to get the k-coproduct completion monad. Mark Weber [For admin and other information see: http://www.mta.ca/~cat-dist/ ]