Axiom G. For every \(\infty \)-category \(C\) there is an opposite category \(C\catop \). Similarly every functor \(F\colon C \to D\) induces an opposite functor \(F\catop \colon C\catop \to D\catop \), and this process respects composition of functors. We have equivalences \((C\catop )\catop \simeq C\) and \((F\catop )\catop \simeq F\).
If \(C\) and \(D\) come from classical 1-categories then \(C\catop \) and \(F\catop \) agree with the usual constructions of opposite categories.
If \(X\) is an anima then we have an equivalence \(X\catop \simeq X\).
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