[schwurb]

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.

[nybble41]

> one the two other important Haskell "design-patterns" (Functor - Applicative - Monad)

These days you should probably add Foldable and Traversable to that list, as they are closely related and appear throughout the standard libraries and even in the Prelude.

Traversable is a generalization of Functor to include Applicative effects. It reduces to Functor if the Applicative happens to be the Identity type.

Where Functor and Traversable replace values one-to-one while preserving structure, Foldable represents reducing operations (folds) which consume the values from a structure in some defined order to build up a result. This includes basic functions like sums and products, as well as more complex operations like `sequence`.

[IshKebab]

> 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.

Hmm well it might break down but simply by choosing a better word you've helped me understand what a monad is more than any article I've read on the matter.