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Transformation double categories associated to 2-group actions
Theory and applications of categories, Tome 30 (2015), pp. 1429-1468

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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.

Publié le :
Classification : 18B40, 18D10, 20L99
Keywords: 2-group, categorical group, crossed module, action, double category, adjoint action 
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     author = {Jeffrey C. Morton and Roger Picken},
     title = {Transformation double categories associated to 2-group actions},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/}
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Jeffrey C. Morton; Roger Picken. Transformation double categories associated to 2-group actions. Theory and applications of categories, Tome 30 (2015), pp. 1429-1468. http://geodesic.mathdoc.fr/item/TAC_2015_30_a42/