6 papers
Induction for extended affine type A Soergel bimodules: first steps
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
In this paper we take the first steps towards the categorification of the Zelevinsky tensor product of finite dimensional representations of extended affine type A Hecke algebras.
Almost finitary birepresentation theory and applications to affine Soergel bimodules
Marco Mackaay, Vanessa Miemietz, Pedro Vaz
In this article, we develop a generalization of finitary birepresentation theory applicable to Soergel bimodules for infinite Coxeter groups. We establish a reduction process for t…
Endomorphisms of cell 2-representations
Volodymyr Mazorchuk, Vanessa Miemietz
We determine the endomorphism categories of cell 2-representations of fiat 2-categories associated with strongly regular two-sided cells under some natural assumptions. Along the w…
Pretriangulated 2-representations via dg algebra 1-morphisms
Robert Laugwitz, Vanessa Miemietz
This paper develops a theory of pretriangulated 2-representations of dg 2-categories. We characterize cyclic pretriangulated 2-representations, under certain compactness assumption…
Hochschild cohomology for finitary 2-representations
James Macpherson, Vanessa Miemietz, Mateusz StroiÅski
In this article, we define and investigate Hochschild cohomology for finitary 2-representations of quasi-fiat 2-categories.
Differential graded cell 2-representations
Robert Laugwitz, Vanessa Miemietz
This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong…