Remark 3.5.3.14. Corollary 3.5.3.13 can be reformulated using the language of Kan extensions (see Definition 7.3.0.1): it asserts that a simplicial set $X_{\bullet }: \operatorname{{\bf \Delta }}^{\operatorname{op}} \rightarrow \operatorname{Set}$ is $n$-coskeletal if and only if it is right Kan extended from the full subcategory of $\operatorname{{\bf \Delta }}^{\operatorname{op}}$ spanned by the objects $\{ [k] \} _{k \leq n}$. Compare with Remark 1.1.3.12.
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