> I'd love a reference to materials explaining the "Eilenberg-Moore category", as explanations I've found are incredibly difficult (especially compared to the Kleisli category, which from a programming perspective is very straightforward to understand).
I don't know what's best, but the Eilenberg-Moore category of a monad is the category of "algebras" of a monad, so you should probably start by getting a good understanding of the algebras of a monad. To mathematicians, the most important thing about monads is their algebras: we describe mathematical structures as algebras of monads.
This might help:
* The Catsters, [Monads 3](https://www.youtube.com/watch?v=eBQnysX7oLI).
This is part of a series of videos by some friends of mine; it might be best to start at the beginning:
* The Catsters, [Monads 1](https://www.youtube.com/watch?v=9fohXBj2UEI&list=PL0E91279846EC843E).