[Haskell-cafe] Re: what is inverse of mzero and return?
Keean Schupke
k.schupke at imperial.ac.uk
Tue Jan 25 06:56:06 EST 2005
Ashley Yakeley wrote:
>Every morphism in any category has a "from" object and a "to" object: it
>is a morphism from object to object. In the "Haskell category", a
>function of type 'A -> B' is a morphism from object (type) A to object B.
>
>But in category theory, just because two morphisms are both from object
>A to object B does not mean that they are the same morphism. And so it
>is for the Haskell category: two functions may both have type 'A -> B'
>without being the same function.
>
>
I guess I am trying to understand how the Monad laws are derived from
category theory...
I can only find referneces to associativity being required.
Monads are defined on functors, so the associativity just requires the
associativity of the
'product' operation on functors...
I guess I don't quite see how associativity of functors (of the category
of functions on types) implies identity on values... surely just the
identity on those functors is required?
Keean.
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