Orthofibration Winges

Remark 16.2.3. Winges in fact shows the stronger claim that this identification of the fibers is natural in both \(C\) and \(D\) simultaneously. Formulating this precisely requires the notion of orthofibrations, which are functors of the form \(E \to C \times D\) that correspond under a generalized form of straightening to functors \(C\catop \times D \to \Cat _{\infty }\). What Winges shows is that the functor \((s,t)\) from Theorem 16.2.2 is the orthofibration classifying the assignment \((C,D) \mapsto \Fun ^{\Oo \dlax }(C,D)\).