[kmill]

That is a question you can ask https://math.stackexchange.com/

Unlike mathoverflow, it is meant for every kind of math question below research level.

(Regarding $\to$ vs $\mapsto$, I think of it as type-level vs lambda expression. I think you can find it in any introductory abstract algebra book that assumes you still need to learn a thing or two about functions.)

In my experience, it seems the usual way people in the math community resolve these issues is to ask an expert, or at least a knowledgeable grad student.