Pyramids and 2-representations

Abstract

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 simple transitive $2$-representation of the $2$-category of projective bimodules over a finite dimensional algebra is equivalent to a cell $2$-representation.

References in corpus (7)

• 2-Kac-Moody algebras
• Simple transitive 2-representations via (co)algebra 1-morphisms
• Special modules over positively based algebras
• Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categories
• Simple transitive 2-representations for two non-fiat 2-categories of projective functors
• Bimodules over uniformly oriented A_n quivers with radical square zero
• Characterisation and applications of $\mathbb{k}$-split bimodules

Cited by in corpus (1)

• Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations