[ShaneWilton]

In my experience, it's more important to know that something isn't a monoid / semilattice / <insert structure here>

The CRDTs linked by the parent are a great example. If you're working on an eventually consistent system, and you see a structure that doesn't form a monoid, it's most likely the case that there's going to be some sort of race condition. That isn't to say that any given monoid is going to solve the problem, but it can definitely help to pinpoint possible problems in otherwise complicated code.

It definitely doesn't come up in every discipline, but studying these structures has improved my engineering a ton. If design patterns are about class and object composition, then I'd argue that algebraic structures are the equivalent for function composition.

Full disclosure: I write mostly functional Erlang code for a living