Corollary 3.5.3.19. Let $n$ be an integer. Then the inclusion functor
\[ \{ \textnormal{$n$-coskeletal simplicial sets} \} \hookrightarrow \operatorname{Set_{\Delta }} \]
admits a left adjoint, given on objects by the construction $X \mapsto \operatorname{cosk}_{n}(X)$.