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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?

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It is a strange state of things were facts are cheap and/or ad-hoc! :) – Mariano Suárez-Alvarez Apr 28 '11 at 17:54
I guess it basically is the way to count obstructions. You use (Co)Homology to measure how far a given object is away from being trivial in a given theory. – Alexander Thumm Apr 28 '11 at 19:20
Qiaochu, that's an answer as far as I'm concerned. Thanks! – Jon Bannon Apr 28 '11 at 19:58

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