More Morphisms between Bundle Gerbes
Konrad Waldorf

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology
