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Group actions on 2-categories.
- Source :
- Manuscripta Mathematica; May2019, Vol. 159 Issue 1/2, p81-115, 35p
- Publication Year :
- 2019
-
Abstract
- 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). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00252611
- Volume :
- 159
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Manuscripta Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 135780371
- Full Text :
- https://doi.org/10.1007/s00229-018-1031-2