What you are describing is a Functor, one the two other important Haskell "design-patterns" (Functor - Applicative - Monad). "Mappable" is a good name insofar as it is more familiar to new folks. However, I like the mathematical name as it forces one to embrace the interface as what it is, as opposed to thinking about Functors as collection of data that can be mapped over. Often this is true, but not always.
A monad could be described as "sequencable/chainable", but that metaphor is quickly breaking down as there as so many ways in which monads show up.
A monad could be described as "sequencable/chainable", but that metaphor is quickly breaking down as there as so many ways in which monads show up.