Indexing of maps in fiber and exact sequences about book

[Alizter]

There is a difference between the indexing in algebraic topology and the one here however. In algebraic topology one might start with 1 as the first natural number, although this seems to be less common than it used to be. Since our natural numbers start with 0, it would be annoying having to special case f^(0). Therefore shifting the indexing by one, let's you have a "cleaner" indexing.

[mikeshulman]

Yeah, I'm inclined to stick with the current convention for that reason. It's not even that the f^n : X^n -> X^(n-1) convention chooses to start with 1 rather than 0, but it's inconsistent about where it starts: the X's start from 0, but the f's start from 1.

[EricWay1024]

Thank you with your responses and I can see the rationale better now. I'll close the issue since nothing needs to be done.