2023/04/14 by Abellán, Fernando, Stern, Walker H.
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2304.07028
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 f:ℂ → \mathbbD an outer 2-Cartesian fibration \mathbbF(ℂ)→ \mathbbD which we identify it as the free fibration on the functor f.