Exercise 4.6.1.24. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an isofibration of simplicial sets, and let $X$ and $Y$ vertices of $\operatorname{\mathcal{C}}$. Show that the induced map $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{D}}}(q(X), q(Y) )$ is a Kan fibration.
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