About two weeks ago I asked this question on MSE: https://math.stackexchange.com/questions/1085946/when-should-i-be-doing-cohomology. (Short version: what are some ways I can tell that some sort of cohomology theory might be relevant to a piece of math not obviously about cohomology already?) It received some interest, but no responses even after I offered a bounty.
I posted it there because I'm fairly certain that it's too elementary for MO; on the other hand, I'm certain there are interesting things that can be said about it. So my question is,
Is the question above appropriate for MO? If not, are there ways I can modify it so it becomes appropriate?
(Of course, regardless of the answer, I'll wait until the MSE bounty expires before doing anything here.)