Artículo
Group actions on 2-categories
Fecha de publicación:
05/2019
Editorial:
Springer
Revista:
Manuscripta Mathematica
ISSN:
0025-2611
e-ISSN:
1432-1785
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups. Associated to a group action on a 2-category, we construct the 2-category of equivariant objects. We also introduce the G-equivariant notions of pseudofunctor, pseudonatural transformation and modification. Our first main result is a coherence theorem for 2-categories with an action of a group. For a 2-category B with an action of a group G, we construct a braided G-crossed monoidal category Z G (B) with trivial component the Drinfeld center of B. We prove that, in the case of a G-action on the 2-category of representation of a tensor category C, the 2-category of equivariant objects is biequivalent to the module categories over an associated G-extension of C. Finally, we prove that the center of the equivariant 2-category is monoidally equivalent to the equivariantization of a relative center, generalizing results obtained in Gelaki et al. (Algebra Number Theory 3(8):959–990, 2009).
Palabras clave:
Categories
,
Groups
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Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Bernaschini, María Eugenia; Galindo, César; Mombelli, Juan Martín; Group actions on 2-categories; Springer; Manuscripta Mathematica; 159; 5-2019; 81-115
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