From: Bas Spitters <spitters@cs.ru.nl>
To: Mike Stay <metaweta@gmail.com>
Cc: categories <categories@mta.ca>
Subject: Re: Haskell Arrows and internal categories
Date: Wed, 29 Sep 2010 14:06:16 +0200 [thread overview]
Message-ID: <E1P15xs-0001ff-8E@mlist.mta.ca> (raw)
In-Reply-To: <E1P0kUW-0003qo-P2@mlist.mta.ca>
You may be interested in the work of my colleagues:
"Categorical semantics for Arrows" (2009) Bart Jacobs, Ichiro Hasuo
and Chris Heunen
Journal of Functional Programming, 19(3-4):403-438, 2009
http://www.comlab.ox.ac.uk/people/chris.heunen/publications/2008/arrows/arrows.pdf
"Arrows, like Monads, are Monoids" (2006) Bart Jacobs and Chris Heunen
(ENTCS 158:219-236) in the proceedings of MFPS 22
http://www.comlab.ox.ac.uk/people/chris.heunen/publications/2006/arrows/arrows.pdf
Bas
On Tue, Sep 28, 2010 at 1:45 AM, Mike Stay <metaweta@gmail.com> wrote:
> On Mon, Sep 27, 2010 at 3:50 PM, Mike Stay <metaweta@gmail.com> wrote:
>> I'm trying to understand Arrows in Haskell,
>> http://www.haskell.org/arrows/index.html
>> but since I haven't become literate yet, I'm not sure I'm getting
>> everything right. It looks to me like an Arrow is a monoidal closed
>> category object in Hask. Is 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 => A
> and dinatural transformations
> - compose:A(b,c) x A(a,b) => A(a,c)
> - first:A(a,b) => A(a tensor c, b tensor c)
> satisfying various coherence laws.
> --
> 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/ ]
next prev parent reply other threads:[~2010-09-29 12:06 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <AANLkTinJEsOLaF4iaMcgJoypZktx4q-AFCpTtmw+5oz=@mail.gmail.com>
2010-09-27 23:45 ` Mike Stay
2010-09-29 12:06 ` Bas Spitters [this message]
2010-09-30 10:24 ` Jeff Egger
2010-09-30 13:39 ` Mike Stay
[not found] ` <AANLkTik1xN6-cDm+0DezF3xfRUhKRrR95ZBiC-zrYj-R@mail.gmail.com>
2010-09-28 17:42 ` Mike Stay
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