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Jul 7, 2023 at 8:21 comment added Adrien I don't know if this is what you're asking, but indeed it seems this is backward: if you're looking at the coordinate algebra $O(G)$ then the coproduct encodes the multiplication of $G$, and then the tensor product in fact matches the multiplication of $O(G)$. In other words algebraic representations of $G$ are $O(G)$-comodules, not modules.
Jul 7, 2023 at 1:34 history asked Justin Bloom CC BY-SA 4.0