Example 7.7.2.16. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits pullbacks. Then a colimit of the empty diagram $F: \emptyset \rightarrow \operatorname{\mathcal{C}}$ can be identified with an initial object $C \in \operatorname{\mathcal{C}}$. In this case, $C$ is a universal colimit of $F$ if and only if it is a strongly universal colimit of $F$: both conditions are equivalent to the requirement that the projection map $\operatorname{\mathcal{C}}_{/C} \rightarrow \Delta ^0$ is an equivalence of $\infty $-categories, or that every morphism $C' \rightarrow C$ is an isomorphism. See Example 7.7.1.17.
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