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.