Example 5.6.1.14. Let $\operatorname{\mathcal{C}}$ be a category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Cat}$ be a functor between ordinary categories, which we can identify with a strict functor from $\operatorname{\mathcal{C}}$ to the $2$-category $\mathbf{Cat}$. Applying Remark 5.6.1.13, we deduce that the category of elements $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ fits into a pullback diagram
\[ \xymatrix@R =50pt@C=50pt{ \int _{\operatorname{\mathcal{C}}} \mathscr {F} \ar [d] \ar [r] & \operatorname{Cat}_{\ast }^{\mathrm{lax}} \ar [d] \\ \operatorname{\mathcal{C}}\ar [r]^-{\mathscr {F}} & \operatorname{Cat}. } \]