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

Volodymyr Mazorchuk, Vanessa Miemietz

Published 2014-08-26Version 1

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.