What are arguments to a monad bind operation formally called?

Question

For example, in the list monad bind operation:

xs >>= f = concat (map f xs)

What is the argument f called? A binder? mapper? transformer?

Answer 1

Sorry to be glib, but the argument is called f, since depending on what it does, one of any number of names could be applicable. What matters, simply, is its type a -> m b for your Monad instance m. As David Yong's comment notes, we can describe things of that form as an "arrow (or morphism) in the Kleisli category of m".