Remark 3.5.8.8. Let $X$ be a Kan complex. Then the morphisms $f_{n}: \pi _{\leq n}(X) \rightarrow \operatorname{cosk}_{n-1}^{\circ }(X)$ of Proposition 3.5.8.7 fit into a commutative diagram
\[ \xymatrix@R =50pt@C=50pt{ \cdots \ar [r] & \operatorname{cosk}_{3}^{\circ }(X) \ar [r] \ar [d] & \operatorname{cosk}_{2}^{\circ }(X) \ar [r] \ar [d] & \operatorname{cosk}_{1}^{\circ }(X) \ar [r] \ar [d] & \operatorname{cosk}_{0}^{\circ }(X) \ar [d] \\ \cdots \ar [r] \ar [ur] & \pi _{\leq 3}(X) \ar [r] \ar [ur]^{f_3} & \pi _{\leq 2}(X) \ar [r] \ar [ur]^{f_2} & \pi _{\leq 1}(X) \ar [ur]^{f_1} \ar [r] & \pi _{\leq 0}(X), } \]
which intertwines the intertwine the canonical Postnikov tower of Example 3.5.8.2 with the weakly coskeletal tower of Example 3.5.8.5.