Kerodon

Example 3.5.7.2. Let $n$ be an integer. Recall that a Kan complex $X$ is $(n+1)$-coskeletal if, for every integer $m \geq n+2$, every morphism of simplicial sets $\operatorname{\partial \Delta }^{m} \rightarrow X$ extends uniquely to an $m$-simplex of $X$ (Definition 3.5.3.1). If this condition is satisfied, then $X$ is $n$-truncated. In particular, every $n$-groupoid is $n$-truncated (Corollary 3.5.5.11). See Proposition 3.5.7.15 (or Variant 3.5.7.16) for a partial converse.