monad - the Category hierachy

 reading the "The Typeclassopedia" by Brent Yorgey in Monad.Reader#13 ,and found that "the Functor hierachy" is interdependent of "the Category hierachy" as the Figure.1 shown.

 

And according to the author, ArrowApply == Monad, especially that the previous one is just a type class instance that can be used when

 

https://stackoverflow.com/questions/8365992/arrow-and-monad-two-independent-viewpoints-to-compose-computations