From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6242 Path: news.gmane.org!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Re: Haskell Arrows and internal categories Date: Mon, 27 Sep 2010 16:45:47 -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 1285720031 14751 80.91.229.12 (29 Sep 2010 00:27:11 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 29 Sep 2010 00:27:11 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Wed Sep 29 02:27:06 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 1P0kVk-0001uw-Sr for gsmc-categories@m.gmane.org; Wed, 29 Sep 2010 02:27:05 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41428) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1P0kUZ-0006sE-Hd; Tue, 28 Sep 2010 21:25:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1P0kUW-0003qo-P2 for categories-list@mlist.mta.ca; Tue, 28 Sep 2010 21:25:49 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6242 Archived-At: On Mon, Sep 27, 2010 at 3:50 PM, Mike Stay wrote: > I'm trying to understand Arrows in Haskell, > =A0 =A0http://www.haskell.org/arrows/index.html > but since I haven't become literate yet, I'm not sure I'm getting > everything right. =A0It looks to me like an Arrow is a monoidal closed > category object in Hask. =A0Is that all there is to it? Hmm. After 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 and dinatural transformations - compose:A(b,c) x A(a,b) =3D> A(a,c) - first:A(a,b) =3D> A(a tensor c, b tensor c) satisfying various coherence laws. --=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/ ]