Warning 3.5.8.11. Let $X$ be a Kan complex. Then the transition maps in the coskeletal tower
\[ \cdots \rightarrow \operatorname{cosk}_{4}(X) \rightarrow \operatorname{cosk}_{3}(X) \rightarrow \operatorname{cosk}_{2}(X) \rightarrow \operatorname{cosk}_{1}(X) \]
are generally not Kan fibrations. See Warning 3.5.4.27.