Principal 2-bundles and their gauge 2-groups

TL;DR

This paper introduces principal 2-bundles, classifies them via non-abelian Cech cohomology, and describes their gauge 2-groups with smooth structures, extending classical bundle theory to higher categories.

Contribution

It develops the theory of principal 2-bundles, their classification, and gauge 2-groups, providing explicit examples and establishing smooth structures.

Findings

Principal 2-bundles are classified by non-abelian Cech cohomology.

Gauge 2-groups can be described by 2-group-valued functors.

Under mild conditions, gauge 2-groups have natural smooth structures.

Abstract

In this paper we introduce principal 2-bundles and show how they are classified by non-abelian Cech cohomology. Moreover, we show that their gauge 2-groups can be described by 2-group-valued functors, much like in classical bundle theory. Using this, we show that, under some mild requirements, these gauge 2-groups possess a natural smooth structure. In the last section we provide some explicit examples.