# Kerodon

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Corollary 7.2.2.3. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $e: A \rightarrow B$ be a left cofinal morphism of simplicial sets. Then a morphism of simplicial sets $\overline{f}: B^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ is a limit diagram if and only if the composite map

$A^{\triangleleft } \xrightarrow {e^{\triangleleft }} B^{\triangleleft } \xrightarrow { \overline{f} } \operatorname{\mathcal{C}}$

is a limit diagram.

Proof. Apply Corollary 7.2.2.2 in the special case $\operatorname{\mathcal{D}}= \Delta ^0$ (see Example 7.1.5.3). $\square$