Bicategorical homotopy fiber sequences

TL;DR

This paper explores the relationship between bicategories and their classifying spaces, extending classical theorems to the bicategorical setting to deepen understanding of their homotopy types.

Contribution

It generalizes Quillen's Theorems A and B to lax functors between bicategories, advancing the theoretical framework of bicategorical homotopy theory.

Findings

Generalized Quillen's Theorems A and B for bicategories

Established connections between bicategories and their classifying spaces

Enhanced understanding of homotopy types in bicategorical contexts

Abstract

Small B\'{e}nabou's bicategories and, in particular, Mac Lane's monoidal categories, have well-understood classifying spaces, which give geometric meaning to their cells. This paper contains some contributions to the study of the relationship between bicategories and the homotopy types of their classifying spaces. Mainly, generalizations are given of Quillen's Theorems A and B to lax functors between bicategories.