Let $(M,\otimes)$ be a small symmetric monoidal category. Is it possible to choose in each isomorphy class $[A]$ a representative $A_0$ and for each $A\in M$ an isomorphism $\phi_A:A\to A_0$ in a way that for any $A,B\in M$ the equation $$ \phi_{A\otimes B}=\phi_{A\otimes B_0}\circ(1\otimes\phi_B) $$ holds?
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