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>> fmap id = id
I think the above identity is not quite right. It has different types on either side of the "=" sign. And I think that's a consequence of the fact that a functor maps the identity of the morphisms of one category to that of another - the two identities belong to different categories, not the same as the above identity indicates.
In the case of lists probably the right identity is
map id = [id]. If I check the types for the list identity
map id :: [b] -> [b]
[id] :: [a -> a]
I'm not quite sure if this makes sense, but it feels right. (I'm a Haskell novice.)
And I have no idea how to express this for general functors.
It is correct.
Hugs> fmap id [1,2,3]
Hugs> id [1,2,3]
Hugs> fmap id [1,2,3] == id [1,2,3]
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