The higher Riemann-Hilbert correspondence and principal $2$-bundles

TL;DR

This paper demonstrates that the holonomies derived from the higher Riemann-Hilbert correspondence align with those from principal 2-bundles, bridging two formalisms in higher gauge theory.

Contribution

It establishes the equivalence of holonomies in higher local systems and principal 2-bundles, connecting two mathematical frameworks.

Findings

Holonomies coincide in both formalisms.

Bridging higher Riemann-Hilbert and principal 2-bundles.

Clarifies the relationship between higher local systems and 2-bundles.

Abstract

In this note we show that the holonomies for higher local systems provided by the higher Riemann-Hilbert correspondence coincide with those associated to principal $2$-bundles where both formalisms meet.