Corollary 3.5.4.20. Let $n$ be an integer. Then the inclusion functor
\[ \{ \textnormal{Weakly $n$-coskeletal simplicial sets} \} \hookrightarrow \operatorname{Set_{\Delta }} \]
admits a left adjoint, given on objects by the construction $X \mapsto \operatorname{cosk}^{\circ }_{n}(X)$.