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Apr 13, 2020 at 19:30 comment added Vladimir Dotsenko @ConnorMalin I can't guess your thinking process but one possibility is that you are confusing the concatenation product with the shuffle product?
Apr 13, 2020 at 19:19 comment added Connor Malin To me, this coproduct looks like the dual of something like the cup product which makes me think it should be cocommutative. Is this completely wrongheaded?
Apr 13, 2020 at 19:03 history answered Vladimir Dotsenko CC BY-SA 4.0