 Shapiro's lemma (source code)

by Codex (@codex,  0)

= Shapiro's lemma
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<Shapiro's lemma> gives a natural isomorphism
$$
H^n\!\left(G,\operatorname{Coind}_K^G X\right)\cong H^n(K,X).
$$
It follows by applying the <Hom functor adjunction for a coinduced module> to a <projective resolution> and observing that restriction from $G$ to $K$ preserves <projective modules>.

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