Definition 3.5.3.15. Let $X$ be a simplicial set and let $n$ be an integer. We will say that a morphism of simplicial sets $f: X \rightarrow Y$ exhibits $Y$ as an $n$-coskeleton of $X$ if it satisfies the following pair of conditions:
The simplicial set $Y$ is $n$-coskeletal.
The morphism $f$ is bijective on $m$-simplices for $m \leq n$.