# Kerodon

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Definition 4.4.1.4. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between $\infty$-categories. We say that $F$ is an isofibration if it is an inner fibration (Definition 4.1.1.1) which satisfies the following additional condition:

$(\ast )$

For every object $C \in \operatorname{\mathcal{C}}$ and every isomorphism $u: D \rightarrow F(C)$ in the category $\operatorname{\mathcal{D}}$, there exists an isomorphism $\overline{u}: \overline{D} \rightarrow C$ in the category $\operatorname{\mathcal{C}}$ satisfying $F(\overline{u}) = u$.