See also the paper "Idioms are oblivious, arrows are meticulous,
monads are promiscuous" [1]. Functors can be extended to give
applicative functors (idioms) which can then be extended to arrows,
and then monads. So all arrows are also (applicative) functors.


[1]: 
http://homepages.inf.ed.ac.uk/wadler/papers/arrows-and-idioms/arrows-and-idioms.pdf
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