Connections on non-abelian Gerbes and their Holonomy

Understand

We introduce an axiomatic framework for the parallel transport of connections on gerbes.

• It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing axioms and smoothness conditions.
• The smoothness conditions are imposed with respect to a strict Lie 2-group, which plays the role of a band, or structure 2-group.
• Upon choosing certain examples of Lie 2-groups, our axiomatic framework reproduces in a systematical way several known concepts of gerbes with connection: non-abelian differential cocycles, Breen-Messing gerbes, abelian and non-abelian bundle gerbes.