Corollary 10.2.4.16 (05H2)

Corollary 10.2.4.16. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories which preserves finite limits and let $n$ be an integer. Then:

$(1)$: If $X_{\bullet }$ is an $n$-coskeletal simplicial object of $\operatorname{\mathcal{C}}$, then $F(X_{\bullet } )$ is an $n$-coskeletal simplicial object of $\operatorname{\mathcal{D}}$.
$(2)$: If $X_{\bullet }$ is an $n$-coskeletal semisimplicial object of $\operatorname{\mathcal{C}}$, then $F( X_{\bullet } )$ is an $n$-coskeletal semisimplicial object of $\operatorname{\mathcal{D}}$.

Proof. Assertion $(2)$ is immediate from the definitions (since the category $\operatorname{\mathcal{J}}$ appearing in the proof of Proposition 10.2.4.15 is a finite partially ordered set). Assertion $(1)$ follows by combining $(2)$ with Proposition 10.2.4.15. $\square$