Group actions on 2-categories View Full Text


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Article Info

DATE

2019-05

AUTHORS

Eugenia Bernaschini, César Galindo, Martín Mombelli

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 ZG(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). More... »

PAGES

1-35

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1007/s00229-018-1031-2

DOI

http://dx.doi.org/10.1007/s00229-018-1031-2

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https://app.dimensions.ai/details/publication/pub.1104378793


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