Transformation Double Categories Associated to 2-Group Actions

Abstract

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.

40 pages. To appear in Theory and Applications of Categories

References in corpus (2)

• Higher-Dimensional Algebra V: 2-Groups
• Higher Gauge Theory: 2-Connections on 2-Bundles

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