Ah, no, you're right. I was thinking that mapping can be f(T1)->T2 and how reducing can change types too, but I guess I wasn't paying enough attention because

Ah, no, you're right. I was thinking that mapping can be f(T1)->T2 and how reducing can change types too, but I guess I wasn't paying enough attention because of course the reduce signature is f(accumulator, input) and the output is accumulator, so yea, you're absolutely right: f(T1,T2)->T1