Hochschild cohomology for finitary 2-representations
In this article, we define and investigate Hochschild cohomology for finitary 2-representations of quasi-fiat 2-categories.
math.RT↗
arXiv subjects
James Macpherson
Publications and source records attributed to James Macpherson.
Evaluation 2-Functors for Kac-Moody 2-Categories of Type A2
We construct a 2-functor from the Kac-Moody 2-category for the extended quantum affine sl(3) to the homotopy 2-category of bounded chain complexes with values in the Kac-Moody 2-category for quantum gl(3), categorifying the evaluation map between the corresponding quantum Kac-Moody algebras.
math.QA↗
2-Representations and Associated Coalgebra 1-Morphisms for Locally Wide Finitary 2-Categories
We define locally wide finitary 2-categories by relaxing the definition of finitary 2-categories to allow infinitely many objects and isomorphism classes of 1-morphisms and infinite dimensional hom-spaces of 2-morphisms. After defining related concepts including transitive 2-representations in this setting, we provide a new method of constructing coalgebra 1-morphisms associated to transitive 2-representations of locally wide weakly fiat 2-categories, and demonstrate that any such transitive 2-representation is equivalent to a certain subcategory of the category of comodule 1-morphisms over the coalgebra 1-morphism. We finish the paper by examining two classes of examples of locally wide weakly fiat 2-categories: 2-categories associated to certain classes of infinite quivers, and singular Soergel bimodules associated to Coxeter groups with finitely many simple reflections.
math.CT↗
Extension Of The 2-Representation Theory Of Finitary 2-Categories To Locally (Graded) Finitary 2-Categories
We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive 2-representations of weakly fiat 2-categories to this environment. We also consider locally finitary 2-categories and 2-representations with a grading, and prove the associated coalgebra 1-morphisms have a homogeneous structure. We use these results to classify simple transitive 2-representations of certain classes of cyclotomic 2-Kac-Moody algebras.
math.CT↗