On cofinal functors of ∞-bicategories

Abstract

In this work, we study the notion of cofinal functor of ∞-bicategories with respect to the theory of partially lax colimits. The main result of this paper is a characterization of cofinal functors of ∞-bicategories via generalizations of the conditions of Quillen's Theorem A. As a key ingredient for the proof of our main theorem we produce for every functor of ∞-bicategories an outer 2-Cartesian fibration which we identify it as the free fibration on the functor.