Corollary 4.5.2.28. Let $F_0: \operatorname{\mathcal{C}}_0 \rightarrow \operatorname{\mathcal{C}}$ and $F_1: \operatorname{\mathcal{C}}_1 \rightarrow \operatorname{\mathcal{C}}$ be functors of $\infty $-categories. If either $F_0$ or $F_1$ is an isofibration, then the comparison map
\[ \operatorname{\mathcal{C}}_0 \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_1 \hookrightarrow \operatorname{\mathcal{C}}_0 \times ^{\mathrm{h}}_{\operatorname{\mathcal{C}}} \operatorname{\mathcal{C}}_1 \quad \quad (C_0, C_1) \mapsto (C_0, C_1, \operatorname{id}) \]
is an equivalence of $\infty $-categories.