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Example Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a right fibration between $\infty $-categories. Then $F$ is an inner fibration (Remark, and any isomorphism $u: D \rightarrow F(C)$ can be lifted to a morphism $\overline{u}: \overline{D} \rightarrow C$ in $\operatorname{\mathcal{C}}$, which is automatically an isomorphism by virtue of Proposition It follows that $F$ is an isofibration. Similarly, any left fibration of $\infty $-categories is an isofibration. For a more general statement, see Corollary