Isn't it a bit strange to have a class with 0 instances in the library?

I suppose we could add an instance for negation of integers?

Looking at the other classes, isn't Involutive R f the same as Cancel R f f?

I was also about to suggest a relation to idempotency, which I thought was something like f (f x) = f x, but it doesn't seem like we have that? We work with such a function a lot though, it's called the core. (Well, things get more complicated because that can also be partial.)

We only have f x x = x, which is an idempotent element of an operation, but not an idempotent operation.

Looking at the other classes, isn't Involutive R f the same as Cancel R f f?

Good point, maybe we should just make it a notation for that?

I was also about to suggest a relation to idempotency,

Not sure if that's worth it.