Corollary 9.3.3.17 (Composition). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing a $2$-simplex
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{ g } & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z, } \]
and let $n$ be an integer. Then:
- $(1)$
If the morphisms $f$ and $g$ are $n$-truncated, then the morphism $h$ is $n$-truncated.
- $(2)$
If the morphism $h$ is $n$-truncated and the morphism $g$ is $(n+1)$-truncated, then the morphism $f$ is $n$-truncated.