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A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...

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An intuitive explanation for group cohomology via cochains?

This should also give you an idea why, in general, The singular cohomology of $BG$ is exactly the group cohomology of $G$. … So, in short: group cohomology is helpful to study groups because it studies the "shape of a group" in the sense of algebraic topology. …
Paolo Perrone's user avatar