Exercise 8.1.3.16. Show that Corollary 8.1.3.15 implies Theorem 8.1.3.14. That is, to prove Theorem 8.1.3.14 in general, it suffices to treat the special case where $\operatorname{\mathcal{D}}$ is a category of the form $[n] = \{ 0 < 1 < \cdots < n\} $ for $n \geq 0$.
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