Variant 3.5.8.10. Let $X$ be a Kan complex. Then the transition maps in the weakly coskeletal tower
\[ \cdots \rightarrow \operatorname{cosk}_{3}^{\circ }(X) \rightarrow \operatorname{cosk}_{2}^{\circ }(X) \rightarrow \operatorname{cosk}_{1}^{\circ }(X) \rightarrow \operatorname{cosk}_{0}^{\circ }(X) \]
are Kan fibrations (whose fibers are homotopy equivalent to Eilenberg-MacLane spaces).