More Morphisms between Bundle Gerbes

TL;DR

This paper introduces new morphisms between bundle gerbes, expanding the 2-category structure and enabling the definition of surface holonomy for various types of surfaces.

Contribution

It defines new 1-morphisms including trivializations and modules, broadening the morphism framework beyond stable isomorphisms.

Findings

Expanded the 2-category of bundle gerbes with new morphisms

Defined surface holonomy for different surface types

Connected morphism structures to surface holonomy concepts

Abstract

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules. They fit into the structure of a 2-category of bundle gerbes, and lead to natural definitions of surface holonomy for closed surfaces, surfaces with boundary, and unoriented closed surfaces.