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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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Universal bundles for monoids versus groups
Dold and Lashof compare their construction for a monoid M to Milnor's
when M is a group G. They give an explicit comparison for the first stage of the constructions. Somewhere I've seen the general n- …