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Suppose we have a monoidal category $\mathbb{C}$, with monoidal product $\otimes$, monoidal unit $I$, left unitor components $I \otimes A \overset{\lambda_A}{\rightarrow} A$ and right unitor components $A \otimes I \overset{\rho_A}{\rightarrow} A$. In this case is it true that $\lambda_I = \rho_I$? If so what is the proof?

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