2013/12/31 by Jeffrey C. Morton, Morton, Jeffrey C., Roger Picken +1 · 1 citation
Computer Science · Mathematics · #18B40 #18D10 #20L99 #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1401.0149
openalex publication_date 2013/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in category-theoretic terms, where symmetry is expressed as the action of a 2-group G (equivalently, a categorical group) on a category C. It describes the construction of a transformation groupoid in diagrammatic terms, and considers this construction internal to Cat, the category of categories. The result is a double category C//G which describes the local symmetries of C. We define this and describe some of its structure, with the adjoint action of G on itself as a guiding example.