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Example 7.5.7.4. Let $\operatorname{\mathcal{C}}$ be a small category and let $\overline{ \mathscr {F} }: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{Set_{\Delta }}$ be a colimit diagram in the category of simplicial sets. If the diagram $\mathscr {F} = \overline{ \mathscr {F} }|_{ \operatorname{\mathcal{C}}}$ is projectively cofibrant, then $\overline{\mathscr {F}}$ is a homotopy colimit diagram: this is a reformulation of Corollary 7.5.6.14 (for a stronger statement, see Corollary 7.5.8.7).