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Dec 22, 2017 at 7:24 vote accept Alexander Braverman
Dec 20, 2017 at 17:45 comment added Tyler Lawson @AlexanderBraverman That's a fair question. The argument above does not quite prove uniqueness, e.g. in the case where $G$ is the discrete group $\Bbb Z/2$, but we also have not used the constraint that $f$ should define an associative multiplication yet. There should be some mileage yet to get out of this.
Dec 20, 2017 at 9:19 comment added Alexander Braverman Thanks. I wonder if this argument can be extended to algebras in more general monoidal categories. For example, rings with $G$-action, where $G$ is some algebraic group.
Dec 19, 2017 at 16:16 history answered Tyler Lawson CC BY-SA 3.0