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gave representation theory a little Idea-section, then added some words on its incarnation as homotopy type theory in context/in the slice over $\mathbf{B}G$ and added the following homotopy type representation theory – table, which I am also including in other relevant entries:
homotopy type theory | representation theory |
---|---|
pointed connected context $\mathbf{B}G$ | ∞-group $G$ |
dependent type | ∞-action/∞-representation |
dependent sum along $\mathbf{B}G \to \ast$ | coinvariants/homotopy quotient |
context extension along $\mathbf{B}G \to \ast$ | trivial representation |
dependent product along $\mathbf{B}G \to \ast$ | homotopy invariants/∞-group cohomology |
dependent sum along $\mathbf{B}G \to \mathbf{B}H$ | induced representation |
context extension along $\mathbf{B}G \to \mathbf{B}H$ | |
dependent product along $\mathbf{B}G \to \mathbf{B}H$ | coinduced representation |
Relevant material happening at the nCafe here.
added pointer to
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