Exercise 2.5.3.6. Let $\operatorname{\mathcal{C}}$ be a differential graded category. Suppose we are given a pair of nondecreasing functions $\alpha : [k] \rightarrow [m]$ and $\beta : [m] \rightarrow [n]$. Show that the function $(\beta \circ \alpha )^{\ast }$ of Proposition 2.5.3.5 coincides with the composition $\alpha ^{\ast } \circ \beta ^{\ast }$.
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