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In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.

4 votes

An intuitive explanation for group cohomology via cochains?

Both answers are wonderful, but I have to admit that there's still some gap between my understanding and why modern topologists think of $BG$ in that way. That being said, you can see why group cocycl …
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1 vote

Unifying "cohomology groups classify extensions" theorems

This is not an answer, but just some pointers to things I guess are related! I posted this in the comments, but it got really messy. So I moved it here. -- original comments below -- I also want to …
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