Kerodon

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Example 4.4.1.2. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor between categories. If $F$ is a fibration in groupoids (or an opfibration in groupoids), then $F$ is an isofibration. For a more general statement, see Example 4.4.1.10.