2013/03/19 by Urs Schreiber, Konrad Waldorf
Mathematics · #Abelian group #Adjoint functors #Advanced Topics in Algebra #Algebra over a field #Axiom #Combinatorics #Computer science #Connection (principal bundle) #Derived functor #Equivalence (formal languages) #Ext functor #Functor #Functor category #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Natural transformation #Path (computing) #Pure mathematics #Topology (electrical circuits) #math.CT #math.GN
paper · pdf · doi:10.1007/s40062-016-0140-4
published as J. Homotopy Relat. Struct. (2016) pp1-42 · 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)
arxiv created 2013/03/19 · openalex publication_date 2016/07/23 · arxiv updated 2017/02/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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.