to instead just look at the formal definition. We'll give that to you below, but it's
sometimes sloganized as
[A monad is just a monoid in the category of endofunctors, what's the problem?](http://stackoverflow.com/questions/3870088).
-Without some intuitive guidance, this can also be unhelpful. We'll try to find a good balance.
+Without some intuitive guidance, this can also be unhelpful. We'll try to find a good balance.
+
+(After you've read this once and are coming back to re-read it to try to digest the details further, the "endofunctors" that slogan is talking about are the boxing operations. Their "monoidal" character is captured in the Monad Laws, where a "monoid"---don't confuse with a mon*ad*---is a simpler algebraic notion, meaning a universe with some associative operation that has an identity. For advanced study, here are some further links on the relation between monads as we're working with them and monads as they appear in category theory:
+[1](http://en.wikipedia.org/wiki/Outline_of_category_theory)
+[2](http://lambda1.jimpryor.net/advanced_topics/monads_in_category_theory/)
+[3](http://en.wikibooks.org/wiki/Haskell/Category_theory)
+[4](https://wiki.haskell.org/Category_theory), where you should follow the further links discussing Functors, Natural Transformations, and Monads.)
+
+
The closest we will come to metaphorical talk is to suggest that
monadic types place values inside of *boxes*, and that monads wrap