A monad is a monoid in the category of endofunctors, what’s the problem?
Knowing that a ring (in abstract algebra) is equivalently defined as "a monoid object in the category of abelian groups" is not going to help you with your first abstract algebra course. It makes things that are glaringly obvious from the usual perspective totally opaque, and means you have to define things like the tensor product of abelian groups properly before you can even define a ring. I don't know of a professor who would even mention this perspective during a first abstract algebra course. You get much a much better intuition for what rings are by just using them.<p>Mathematicians who work in category theory have often seen many, many examples of algebraic structures before they get abstracted away to "a monoid object in the category of blah", and many mathematicians still find it an exercise to unpack these compact definitions back to something more intuitive, or more familiar. And even so, most of the time identifying your favourite object as some abstract category thing doesn't bring anything new or useful to the table for the study of that object. (It can help spot patterns between objects though).<p>I say this for any aspiring Haskell programmers: don't feel like understanding this statement will make you a better programmer. The best way to get better at using monads is to just use monads more, and play around with them. Tracking down all the definitions in the statement is a neat exercise, though.