Variant 4.5.6.10. If $X$ is a Kan complex, then the weakly coskeletal tower
\[ \cdots \rightarrow \operatorname{cosk}_{3}^{\circ }(X) \rightarrow \operatorname{cosk}_{2}^{\circ }(X) \rightarrow \operatorname{cosk}_{1}^{\circ }(X) \rightarrow \operatorname{cosk}_{0}^{\circ }(X) \]
of Example 3.5.8.5 is an isofibrant diagram (Variant 3.5.8.10). Beware that the coskeletal tower
\[ \cdots \rightarrow \operatorname{cosk}_{4}(X) \rightarrow \operatorname{cosk}_{3}(X) \rightarrow \operatorname{cosk}_{2}(X) \rightarrow \operatorname{cosk}_{1}(X) \]
is generally not isofibrant (Warning 3.5.8.11).