Homotopy Fibre Sequences Induced by 2-Functors

TL;DR

This paper explores the connection between 2-categories and their classifying spaces, extending key theorems to the context of 2-functors to deepen understanding of their homotopy types.

Contribution

It generalizes Quillen's Theorem B and Thomason's Homotopy Colimit Theorem to 2-functors, advancing the theoretical framework linking 2-categories and homotopy theory.

Findings

Generalized Quillen's Theorem B to 2-functors

Extended Thomason's Homotopy Colimit Theorem to 2-functors

Provided new insights into the homotopy types of classifying spaces

Abstract

This paper contains some contributions to the study of the relationship between 2-categories and the homotopy types of their classifying spaces. Mainly, generalizations are given of both Quillen's Theorem B and Thomason's Homotopy Colimit Theorem to 2-functors.