Warning 3.5.4.27. Let $X$ be a Kan complex. For every integer $n$, we have a commutative diagram
\[ \xymatrix@R =50pt@C=50pt{ X \ar [rr]^{u} \ar [dr]_{v} & & \operatorname{cosk}^{\circ }_{n}(X) \\ & \operatorname{cosk}_{n+1}(X) \ar [ur]_{q} & } \]
where $u$ is a Kan fibration (Proposition 3.5.4.26) and $q$ is a trivial Kan fibration (Proposition 3.5.4.22). Beware that $v$ is usually not a Kan fibration.