On Functors

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rajiv Permalink
January 16, 2012, 18:13

>> 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.

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January 16, 2012, 19:32

It is correct.

Hugs> fmap id [1,2,3]
[1,2,3]
Hugs> id [1,2,3]
[1,2,3]
Hugs> fmap id [1,2,3] == id [1,2,3]
True
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