Exercise 10.2.6.5. Let $\operatorname{\mathcal{C}}$ be an ordinary category and let $X_{\bullet }$ be an augmented simplicial object of $\operatorname{\mathcal{C}}$. Show that the construction of Remark 10.2.6.4 determines a bijection from the set of splittings of $X_{\bullet }$ (in the sense of Definition 10.2.6.3) to the collection of systems $\{ h_{n}: X_{n} \rightarrow X_{n+1} \} _{n \geq -1}$ satisfying the identities (10.11) and (10.14).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$