2022/03/22 by Ralf Meyer, Meyer, Ralf · 2 citations
Mathematics · #18A30 #18B40 #18N10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2203.12068
openalex publication_date 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A diagram of groupoid correspondences is a homomorphism to the bicategory of étale groupoid correspondences. We study examples of such diagrams, including complexes of groups and self-similar higher-rank graphs. We encode the diagram in a single groupoid, which we call its groupoid model. The groupoid model is defined so that there is a natural bijection between its actions on a space and suitably defined actions of the diagram. We describe the groupoid model in several cases, including a complex of groups or a self-similar group. We show that the groupoid model is a bilimit in the bicategory of groupoid correspondences.