Warning 5.6.2.11. Let $\operatorname{\mathcal{C}}$ be an $(\infty ,2)$-category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{ \pmb {\mathcal{QC}} }$ be a morphism of simplicial sets. If $\mathscr {F}$ is not a functor, then $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ need not be an $(\infty ,2)$-category (this phenomenon arises already in the case $\operatorname{\mathcal{C}}= \Delta ^2$).
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