A relative 2-nerve

In this work, we introduce a 2-categorical variant of Lurie’s relative nerve functor. We prove that it defines a right Quillen equivalence which, upon passage to $\mathrm{\infty }$-categorical localizations, corresponds to Lurie’s scaled unstraightening equivalence. In this $\mathrm{\infty }$-bicategorical context, the relative 2-nerve provides a computationally tractable model for the Grothendieck construction which becomes equivalent, via an explicit comparison map, to Lurie’s relative nerve when restricted to 1-categories.