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Is there a complex coalgebra $C$ with dimension at least 2 for which the scalar operators $T(x)=\lambda x$ are the only operators which satisfy $$(T\otimes T)\circ \Delta= \Delta \circ T^{2}$$

This equation is motivated by the fact that the differentiation operator $T=d/dx$ on complex coalgebra $\mathbb{C}[x]$ satisfies this equation.

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