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Moscow Mathematical Journal, 2014, Volume 14, Number 3, Pages 595–615
DOI: https://doi.org/10.17323/1609-4514-2014-14-3-595-615 (Mi mmj534) 		 
This article is cited in 40 scientific papers (total in 40 papers)

Additive versus abelian $2$-representations of fiat $2$-categories

Volodymyr Mazorchuka, Vanessa Miemietzb

a Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden
b School of Mathematics, University of East Anglia, Norwich, UK, NR4 7TJ
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DOI: https://doi.org/10.17323/1609-4514-2014-14-3-595-615
Abstract: We study connections between additive and abelian $2$-representations of fiat $2$-categories, describe combinatorics of $2$-categories in terms of multisemigroups and determine the annihilator of a cell $2$-representation. We also describe, in detail, examples of fiat $2$-categories associated to $\mathfrak{sl}_2$-categorification in the sense of Chuang and Rouquier, and $2$-categorical analogues of Schur algebras.
Key words and phrases: $2$-category, $2$-representation, functor, natural transformation, additive category, abelian category.
Received: January 10, 2012; in revised form February 26, 2014
Bibliographic databases:
Document Type: Article
MSC: 18D05, 18E05, 17B10
Language: English
Citation: Volodymyr Mazorchuk, Vanessa Miemietz, “Additive versus abelian $2$-representations of fiat $2$-categories”, Mosc. Math. J., 14:3 (2014), 595–615
Citation in format AMSBIB
\Bibitem{MazMie14}
\by Volodymyr~Mazorchuk, Vanessa~Miemietz
\paper Additive versus abelian $2$-representations of fiat $2$-categories
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 3
\pages 595--615
\mathnet{http://mi.mathnet.ru/mmj534}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-3-595-615}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241761}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000342789400007}
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    • This publication is cited in the following 40 articles:
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