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Homotopical interpretation of Langlands correspondence

Recently I began learning about homotopy theory, I am very far from being familiar with all the basic notions and constructions, however I heard of the notion of topological modular forms. I also ...
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Does the category of G-spectra know G?

I was recently in the situation of having access to the category of $G$-modules (for some group $G$ which I had forgotten), as just a category, i.e. no monoidal structure, together with the forgetful ...