Remark 15.2.9. Note that all the steps in the construction of \(\OpCocart _C = (C^{\amalg },p_C^{\amalg })\) are functorial in \(C\). Using Proposition 15.1.9, we may write it as the composite \[ \Cat _{\infty } \iso \Fun ^{\times }(\Fin \catop ,\Cat _{\infty }) \xrightarrow {\Un ^{\ct }} \Cart (\Fin ) \xrightarrow {E \mapsto (E,E^{p\dcart },E)} \AdTrip _{/\Fin } \xrightarrow {\Span } (\Cat _{\infty })_{/\Span (\Fin )}. \] In particular, we obtain a functor \[ \OpCocart \colon \Cat _{\infty } \to \Op _{\infty }. \]
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