28 Sep
2010
28 Sep
'10
5:42 p.m.
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/ ]