From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6248 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Haskell Arrows and internal categories Date: Tue, 28 Sep 2010 10:42:44 -0700 Message-ID: References: Reply-To: Mike Stay 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: dough.gmane.org 1285802030 7641 80.91.229.12 (29 Sep 2010 23:13:50 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 29 Sep 2010 23:13:50 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Thu Sep 30 01:13:46 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1P15qG-0003Io-5r for gsmc-categories@m.gmane.org; Thu, 30 Sep 2010 01:13:40 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40472) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P15p1-0000O4-3K; Wed, 29 Sep 2010 20:12:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P15ow-0001Rd-6g for categories-list@mlist.mta.ca; Wed, 29 Sep 2010 20:12:18 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6248 Archived-At: On Mon, Sep 27, 2010 at 4:45 PM, Mike Stay wrote: > Hmm. =A0After reading "Freyd is Kleisli, for Arrows", it now looks to me > like an Arrow is an enrichment. > > It consists of a V-profunctor > - A:C^op x C -> V, > where V is a monoidal category, together with a natural transformation > - arr:Hom =3D> A It was pointed out to me that this doesn't make sense unless C is already V-enriched (which was the case in the two examples I saw, Set and Hask), but if we have a monoidal functor i:Set -> V, then we can define - arr:i Hom =3D> A. --=20 Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]