# Diagrams and discrete extensions for finitary 2-representations

@article{Chan2017DiagramsAD, title={Diagrams and discrete extensions for finitary 2-representations}, author={Aaron Chan and Volodymyr Mazorchuk}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2017}, volume={166}, pages={325 - 352} }

Abstract In this paper we introduce and investigate the notions of diagrams and discrete extensions in the study of finitary 2-representations of finitary 2-categories.

## 28 Citations

### Simple transitive 2-representations of 2-categories associated to self-injective cores

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- MathematicsIndiana University Mathematics Journal
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For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using coalgebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also…

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We apply the theory of weighted bicategorical colimits to study the problem of existence and computation of such colimits of birepresentations of finitary bicategories. The main application of our…

### COIDEMPOTENT SUBCOALGEBRAS AND SHORT EXACT SEQUENCES OF FINITARY 2-REPRESENTATIONS

- MathematicsNagoya Mathematical Journal
- 2020

In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and…

### Pyramids and 2-representations

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We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every…

### Classification problems in 2-representation theory

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This article surveys recent advances and future challenges in the 2-representation theory of finitary 2-categories with a particular emphasis on problems related to classification of various classes…

### Simple transitive 2-representations of left cell 2-subcategories of projective functors for star algebras

- MathematicsCommunications in Algebra
- 2019

Abstract In this article, we study simple transitive 2-representations of certain 2-subcategories of the 2-category of projective functors over a star algebra. We show that in the simplest case,…

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We use the Perron-Frobenius Theorem to define, study and, in some sense, classify special simple modules over arbitrary finite dimensional positively based algebras. For group algebras of finite Weyl…

### On Simple Transitive 2-representations of Bimodules over the Dual Numbers

- MathematicsAlgebras and Representation Theory
- 2022

We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations…

### 2-categories of symmetric bimodules and their 2-representations

- MathematicsPacific Journal of Mathematics
- 2020

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under…

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