Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories

Abstract

We introduce the class of isotypic $2$-representations for finitary $2$-categories and the notion of inflation of $2$-representations. Under some natural assumptions we show that isotypic $2$-representations are equivalent to inflations of cell $2$-representations.

to appear in Math Z

References in corpus (3)

• 2-Kac-Moody algebras
• Transitive 2-representations of finitary 2-categories
• Categorification of tensor product representations of sl(k) and category O

Cited by in corpus (5)

• 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
• Duflo involutions for 2-categories associated to tree quivers
• Multisemigroups with multiplicities and complete ordered semi-rings
• Sub-bimodules of the identity bimodule for cyclic quivers