Integration of 2-term representations up to homotopy via 2-functors

2016/08/02 by Cristián Ortiz, Ortiz, Cristian, Olivier Brahic +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1608.00664

openalex publication_date 2016/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a representation up to homotopy of a Lie algebroid on a 2-term complex of vector bundles, we define the corresponding holonomy as a strict 2-functor from a Weinstein path 2-groupoid to the gauge 2-groupoid of the underlying 2-term complex. We construct a corresponding transformation 2-groupoid and we prove that the 1-truncation of this 2-groupoid is isomorphic to the Weinstein groupoid of the VB-algebroid associated to a representation up to homotopy. As applications, we describe alternative integration schemes for semi-direct products of Lie 2-algebras and string algebras.

Related

• Integration of semidirect product Lie 2-algebras
• Representations up to homotopy of Lie algebroids
• Representation up to homotopy of Hom-Lie algebroids
• Integrating Lie algebroids via stacks and applications to Jacobi manifolds
• Lie II theorem for Lie algebroids via higher groupoids