Remark 3.5.8.6. Let $X$ be a Kan complex. Then the Postnikov towers described in Examples 3.5.8.2, 3.5.8.4, and 3.5.8.5 are related by a commutative diagram
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\begin{equation} \begin{gathered}\label{equation:comparison-of-towers} \xymatrix@R =50pt@C=50pt{ \cdots \ar [r] & \operatorname{cosk}_{4}(X) \ar [r] \ar [d] & \operatorname{cosk}_{3}(X) \ar [r] \ar [d] & \operatorname{cosk}_{2}(X) \ar [r] \ar [d] & \operatorname{cosk}_{1}(X) \ar [d] \\ \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] & \pi _{\leq 3}(X) \ar [r] & \pi _{\leq 2}(X) \ar [r] & \pi _{\leq 1}(X) \ar [r] & \pi _{\leq 0}(X), } \end{gathered} \end{equation}
where the vertical maps are trivial Kan fibrations (see Proposition 3.5.4.22 and Corollary 3.5.6.14).