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Aug 30, 2016 at 16:19 comment added user84144 So above in the question I ask if a symmetric multiplication on $C$ automatically induces one on $C^{hG}$, which coincides with the one coming from topology via $C^{hG} = C^*(X/G)$ when $C = C^*(X)$, and if so how to describe it.
Aug 30, 2016 at 16:12 comment added David C You're welcome. Can you be more precise?
Aug 30, 2016 at 15:59 comment added user84144 This is great! Do these also address the question of whether such a structure automatically descends to a symmetric product on the homotopy invariants of a chain complex?
Aug 30, 2016 at 9:21 history answered David C CC BY-SA 3.0