Kerodon

Example 4.4.1.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\operatorname{\mathcal{D}}$ be an ordinary category. By virtue of Proposition 4.1.1.10, every functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{D}})$ is automatically an inner fibration. If every isomorphism in $\operatorname{\mathcal{D}}$ is an identity morphism, then $F$ is also an isofibration. In particular, every functor of $\infty $-categories $\operatorname{\mathcal{C}}\rightarrow \Delta ^ n$ is automatically an isofibration.