[Haskell-cafe] Re: Why monoids will abide...

Mauro J. Jaskelioff mjj at Cs.Nott.AC.UK
Wed Jan 21 11:15:23 EST 2009

Andrzej Jaworski wrote:
> Monads are monoids in categories of functors C -> C Arrows are monoids
> in subcategories of bifunctors (C^op) x C -> C   Trees are a playing
> ground for functors in general:-)
This is the nice thing about category theory! plenty of reuse of concepts :)

The situation for Arrows is a bit more complex. Monoids (C^op) x C -> C
are equivalent to Freyd categories (Heunen and Jacobs, MFPS 2006) , but
Arrows in Haskell are actually indexed-Freyd categories, as explained by
Bob Atkey in "What is a Categorical Model of Arrows?"
(MSFP 2008, http://homepages.inf.ed.ac.uk/ratkey/arrows.pdf)

The realization that monads are monoids would be far more useful in a
language with kind polymorphism.
However, this shouldn't stop us from dreaming...

All the best,

- Mauro

This message has been checked for viruses but the contents of an attachment
may still contain software viruses, which could damage your computer system:
you are advised to perform your own checks. Email communications with the
University of Nottingham may be monitored as permitted by UK legislation.

More information about the Haskell-Cafe mailing list