Example 10.2.4.11. Let $X_{\bullet }$ be a simplicial set and let $n$ be an integer. The following conditions are equivalent:
The simplicial set $X_{\bullet }$ is $n$-coskeletal in the sense of Definition 3.5.3.1: that is, the restriction map $\operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \Delta ^{m}, X ) \rightarrow \operatorname{Hom}_{\operatorname{Set_{\Delta }}}( \operatorname{\partial \Delta }^{m}, X)$ is bijective for $m > n$.
The simplicial set $X_{\bullet }$ is $n$-coskeletal in the sense of Definition 10.2.4.9: that is, it is a right Kan extension of its restriction to (the opposite of) the subcategory $\operatorname{{\bf \Delta }}^{\leq n} \subset \operatorname{{\bf \Delta }}$.
This is a restatement of Corollary 3.5.3.13 (see Remark 3.5.3.14).