On 24 Jan 2005, at 18:18, Keean Schupke wrote:
Ashley Yakeley wrote:
If you remember your category theory, you'll recall that two morphisms are not necessarily the same just because they're between the same two objects. For instance, the objects may be sets, and the morphisms may be functions between sets: morphisms from A to B are the same only if they map each element in A to the same element in B.
Yes, but I though the 'objects' in this case are endofunctors from a type to itself... the the morphisms operate on these endofunctors, the morphisms are unit and join.... such that joining 'unit' to the endofuntor retults in the endofunctor.
But I think that as the endofunctor is from the type to itself, the value does not
come into it.
I've lost track of what you mean by 'this case' and indeed of what you mean by 'join' (did you mean mplus? the word join is normally used for the operation of type m (m a) -> m a, which is not often used directly in haskell)
However, even addressing your point about endofunctors: for two endofunctors to be equal, they must be equal on all objects and all morphisms, which effectively means they must be pointwise equal on all values.
Jules
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