From: Mike Stay <metaweta@gmail.com>
To: categories <categories@mta.ca>
Subject: Re: Haskell Arrows and internal categories
Date: Tue, 28 Sep 2010 10:42:44 -0700 [thread overview]
Message-ID: <E1P15ow-0001Rd-6g@mlist.mta.ca> (raw)
In-Reply-To: <AANLkTik1xN6-cDm+0DezF3xfRUhKRrR95ZBiC-zrYj-R@mail.gmail.com>
On Mon, Sep 27, 2010 at 4:45 PM, Mike Stay <metaweta@gmail.com> wrote:
> 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
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 => A.
--
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/ ]
prev parent reply other threads:[~2010-09-28 17:42 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
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 [this message]
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