Additive versus abelian 2-representations of fiat 2-categories

Volodymyr Mazorchuk; Vanessa Miemietz

Additive versus abelian 2-representations of fiat 2-categories

Volodymyr Mazorchuk, Vanessa Miemietz

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

46 Citations (Scopus)

92 Downloads (Pure)

Abstract

We study connections between additive and abelian 2-rep-
resentations 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 sl2-categorification in the sense of Chuang and Rouquier,
and 2-categorical analogues of Schur algebras.

Original language	English
Pages (from-to)	595–615
Number of pages	21
Journal	Moscow Mathematical Journal
Volume	14
Issue number	3
Publication status	Published - 2014

Keywords

2-category
2-representation
functor
natural transformation
additive category
abelian category

Access to Document

pdfAccepted author manuscript, 185 KB

http://www.mathjournals.org/mmj/2014-014-003/2014-014-003-007.html

Cite this

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title = "Additive versus abelian 2-representations of fiat 2-categories",

abstract = "We study connections between additive and abelian 2-rep-resentations of fiat 2-categories, describe combinatorics of 2-categoriesin terms of multisemigroups and determine the annihilator of a cell 2-representation. We also describe, in detail, examples of fiat 2-categoriesassociated to sl2-categorification in the sense of Chuang and Rouquier,and 2-categorical analogues of Schur algebras.",

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AU - Mazorchuk, Volodymyr

AU - Miemietz, Vanessa

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AB - We study connections between additive and abelian 2-rep-resentations of fiat 2-categories, describe combinatorics of 2-categoriesin terms of multisemigroups and determine the annihilator of a cell 2-representation. We also describe, in detail, examples of fiat 2-categoriesassociated to sl2-categorification in the sense of Chuang and Rouquier,and 2-categorical analogues of Schur algebras.

KW - 2-category

KW - 2-representation

KW - functor

KW - natural transformation

KW - additive category

KW - abelian category

M3 - Article

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VL - 14

SP - 595

EP - 615

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 3

ER -