A colleague once disparaged his own research to me by saying that it didn't involve any sort of cohomology.
It does, in fact, seem like homological ideas appear across disciplines...and are considered to be mathematically "sexy". I wonder what the deep reason for this is? (The answer "because these ideas prove many things" seems cheap, or ad-hoc here.)
Where can I find a "bird's eye" modern view of general homology/cohomology?