[xupybd]

That could be it. Perhaps my lack of understanding of category theory means I've only developed the pattern recognition for monads but not a deep understanding. So I can only explain it as the abstract thing all of these things have.

[schwurb]

I am gonna be heavily opinionated, take my words with a bit of salt ;)

Here it goes:

1. One understood monads when one is able to write a monadic interface that behaves like any intermediate haskell would expect it to behave. This is not a hard task.

2. Screw the abstract stuff. While fascinating, really few people understand concepts going from abstract to concrete rather than the other way around. And don't get me wrong, I don't think these kind of people are better theorists or problem solvers, they just have to seem a special relationship with symbols. If you are one of those people, you would likely know - in any case, I would encourage to write 3-5 examples of monads in Haskell or Java or JavaScript or whatever language suits you and go from there.