Homotopy colimits of 2-functors

TL;DR

This paper extends classical theorems in algebraic topology and K-theory to the setting of 2-categories, analyzing homotopy colimits of 2-functors and their classifying spaces.

Contribution

It generalizes well-known homotopy colimit theorems to 2-categories, providing a higher categorical framework for these foundational results.

Findings

Extended Homotopy Invariance to 2-categories

Generalized Thomason's Homotopy Colimit Theorem

Unified classical theorems in a 2-categorical context

Abstract

Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical analogues that have been classically used in algebraic topology and algebraic K-theory, such as the Homotopy Invariance Theorem (by Bousfield and Kan), the Homotopy Colimit Theorem (Thomason), Theorems A and B (Quillen), or the Homotopy Cofinality Theorem (Hirschhorn).