This is a great summary. I think it's valuable to say that learning how to map your problem domain onto instances of categories like Monoid is useful because it

This is a great summary. I think it's valuable to say that learning how to map your problem domain onto instances of categories like Monoid is useful because it immediately makes your problem embarassingly parallel, because you can parallelize the addition process (just making sure to preserve overall ordering of operations). I.e., map/reduce. And if it's a commutative monoid, you don't even have to sweat the ordering.