Opposites of finite ∞-categories

Remark 4.2.23. There is a functor \((-)\catop \colon \Cat _{\infty } \to \Cat _{\infty }\) implementing the assignment \(C \mapsto C\catop \). This functor is an equivalence, hence in particular preserves pushouts and full subcategories. Since each of the \(\infty \)-categories \(\emptyset \), \(*\) and \([1]\) are equivalent to their opposites, it follows that an \(\infty \)-category \(C\) is finite if and only if its opposite \(C\catop \) is finite.