Homotopies and automorphisms of crossed modules of groupoids

2000/08/16 by Ronald Brown, R. Brown, Brown, R. +3
Mathematics · #18D15 #18D35 #20L05 #55D15 #55U99 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18D15 #msc:18D35 #msc:20L05 #msc:55D15 #msc:55U99

paper · pdf · doi:10.48550/arxiv.math/0008117

19 pages, A4 size,LaTeX2E,xypic New version December 10, 2001. To appear in Applied Categorical Structures

openalex publication_date 2000/08/16 · arxiv created 2001/12/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere (see math.DG/0009082).

Related

• Homotopies of Lie Crossed Module Morphisms
• Crossed extensions and equivalences of topological 2-groupoids
• Crossed modules and the homotopy 2-type of a free loop space
• The Category of Crossed Modules of Crossed Modules and Its Associated Double Groupoids
• Computation and Homotopical Applications of Induced Crossed Modules