Quillen's Theorem A and the Whitehead theorem for bicategories

TL;DR

This paper extends Quillen's Theorem A to bicategories and demonstrates that a pseudofunctor is a biequivalence if it satisfies certain essential surjectivity, fullness, and faithfulness conditions.

Contribution

It provides a bicategorical analogue of Quillen's Theorem A and characterizes biequivalences via properties of pseudofunctors.

Findings

Established a bicategorical version of Quillen's Theorem A.

Proved that pseudofunctors are biequivalences under specific conditions.

Connected the result to well-known criteria for biequivalence.

Abstract

We prove a bicategorical analogue of Quillen's Theorem A. As an application, we deduce the well-known result that a pseudofunctor is a biequivalence if and only if it is essentially surjective on objects, essentially full on 1-cells, and fully faithful on 2-cells.