# Kerodon

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Definition 4.5.6.3. Let $\operatorname{\mathcal{C}}$ be a small category. We say that a diagram $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ is isofibrant if it satisfies the following condition:

$(\ast )$

Let $\mathscr {E}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$ be a functor and let $\mathscr {E}_0 \subseteq \mathscr {E}$ be a subfunctor for which the inclusion $\mathscr {E}_0 \hookrightarrow \mathscr {E}$ is a levelwise categorical equivalence. Then every natural transformation $\alpha _0: \mathscr {E}_0 \rightarrow \mathscr {F}$ admits an extension $\alpha : \mathscr {E} \rightarrow \mathscr {F}$.