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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.

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An intuitive explanation for group cohomology via cochains?

See section 3 here https://ncatlab.org/nlab/show/group+cohomology, and read https://en.wikipedia.org/wiki/Nerve_(category_theory). A group is thought of as a category with 1 object and morphisms corr …
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