# Kerodon

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Example 4.1.5.6. Let $f: X \hookrightarrow S$ be a monomorphism of simplicial sets, so that the relative diagonal $\delta : X \hookrightarrow X \times _{S} X$ is an isomorphism. Then $f$ is an inner fibration if and only if it is an inner covering. In particular, if $\operatorname{\mathcal{C}}$ is an $\infty$-category and $\operatorname{\mathcal{C}}_0 \subseteq \operatorname{\mathcal{C}}$ is subcategory, then the inclusion map $\operatorname{\mathcal{C}}_0 \hookrightarrow \operatorname{\mathcal{C}}$ is an inner covering.