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Isomorphism between Weyl and Cartan models as Hom-Tensor Adjunction

Let $M$ be a manifold, $\Omega$ be the de Rham complex of $M$. Let $G$ is a compact Lie group acting on $M$, $\mathfrak g$ its Lie algebra and $W(\mathfrak g) = \Lambda(\mathfrak g^*) \otimes S(\...
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