[Haskell-cafe] Article review: Category Theory

Ulf Norell ulfn at cs.chalmers.se
Thu Jan 18 09:05:49 EST 2007

On Jan 16, 2007, at 7:22 PM, David House wrote:

> Hey all,
> I've written a chapter for the Wikibook that attempts to teach some
> basic Category Theory in a Haskell hacker-friendly fashion.
> http://en.wikibooks.org/wiki/Haskell/Category_theory

In the section on the category laws you say that the identity =20
morphism should satisfy

   f . idA =3D idB . f

This is not strong enough. You need

   f . idA =3D f =3D idB . f

Unfortunately, fixing this means that the category Hask is no longer =20
a category since

   _|_ . id =3D \x -> _|_ =AD _|_

Also it's a bit strange to state that morphisms are closed under =20
composition after the associativity law. Wouldn't it be nicer to =20
introduce composition as a total operation off the bat?

/ Ulf

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