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/ ]