Abstract In this work, we conclude our study of fibred -bicategories by providing a Grothendieck construction in this setting. Given a scaled simplicial set S (which need not be fibrant) we construct a 2-categorical version of Lurie’s straightening-unstraightening adjunction, thereby furnishing an equivalence between the -bicategory of 2-Cartesian fibrations over S and the -bicategory of contravariant functors with values in the -bicategory of -bicategories. We provide a relative nerve construction in the case where the base is a 2-category, and use this to prove a comparison to existing bicategorical Grothendieck constructions.
Abellan et al. (Tue,) studied this question.