From: Mike Stay <metaweta@gmail.com>
To: categories <categories@mta.ca>
Subject: Re: Haskell Arrows and internal categories
Date: Mon, 27 Sep 2010 16:45:47 -0700 [thread overview]
Message-ID: <E1P0kUW-0003qo-P2@mlist.mta.ca> (raw)
In-Reply-To: <AANLkTinJEsOLaF4iaMcgJoypZktx4q-AFCpTtmw+5oz=@mail.gmail.com>
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 parent reply other threads:[~2010-09-27 23:45 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 [this message]
2010-09-29 12:06 ` Bas Spitters
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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