In this article we discuss local aspects of 2-functors defined on the path 2-groupoid of a smooth manifold; in particular, local trivializations and descent data. This is a contribution to a project that provides an axiomatic formulation of connections on (possibly non-abelian) gerbes in terms of 2-functors. The main result of this paper establishes the first part of this formulation: we prove an equivalence between the globally defined 2-functors and their locally defined descent data. The second part appears in a separate publication; there we prove equivalences between descent data, on one side, and various existing versions of gerbes with connection on the other side.
- Pub Date:
- March 2013
- Mathematics - General Topology;
- Mathematics - Category Theory
- 47 pages. The content of this paper originally formed the Sections 1 and 2 of our paper "Connections on Non-Abelian Gerbes and their Holonomy" (arxiv:0808.1923)