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Let's take the top left square. We can rewrite it as $$\require{AMScd} \begin{CD} X_1^*\otimes 1\otimes 1 @>{id\otimes id\otimes c_1}>> X_1^*\otimes 1\otimes (X\otimes X_1^*)\\ @V{id\otimes c_2\otimes id}VV @V{id\otimes c_2\otimes id}VV \\ X_1^*\otimes (X\otimes X_2^*)\otimes 1 @>{id\otimes id\otimes c_1}>> X_1^*\otimes(X\otimes ...



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