Today, a talk by Henning Kerstan ("Trace Semantics for Probabilistic Transition Systems") confronted me with category theory for the first time. He has built a theoretical framework for describing probablistic transition systems and their behaviour in a general way, i.e. with uncountably infinite state sets and different notions of traces. To this end, he goes up through several layers of abstraction to finally end up with the notion of monads which he combines with measure theory to build the model he needs.
In the end, it took him 45 minutes to (roughly) build a framework to describe a concept he initially explained in 5 minutes. I appreciate the beauty of the approach (it does generalise nicely over different notions of traces) but it strikes me as an odd balance nevertheless.
I struggle to see what a monad really is and how so general a concept can be useful in applications (both in theory and practice). Is it really worth the effort, result-wise?
Therefore this question:
Are there problems that are natural (in the sense of CS) on which the abstract notion of monads can be applied and helps (or is even instrumental) to derive desired results (at all or in a nicer way than without)?