Simple transitive 2-representations via (co)algebra 1-morphisms

Coalgebra-to-Algebra Morphisms

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

Deformations of Coalgebra Morphisms

An algebraic deformation theory of coalgebra morphisms is constructed.

Coalgebra Morphisms Subsume Open Maps

Simple Transitive 2-Representations of Soergel Bimodules in Type B2

We prove that every simple transitive 2-representation of the fiat 2-category of Soergel bimodules (over the coinvariant algebra) in type B2 is equivalent to a cell 2-representation. We also describe some general properties of the 2-category of Soergel bimodules for arbitrary finite Dihedral groups.

Transitive 2-representations of Finitary 2-categories

In this article, we define and study the class of simple transitive 2-representations of finitary 2-categories. We prove a weak version of the classical Jordan-Hölder Theorem where the weak composition subquotients are given by simple transitive 2-representations. For a large class of finitary 2-categories we prove that simple transitive 2-representations are exhausted by cell 2-representations...