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.
Keywords: 2-category, bundle gerbe, holonomy
2000 MSC: 55R65, 53C29, 18B40
Theory and Applications of Categories,
Vol. 18, 2007,
No. 9, pp 240-273.