Abstract:In this talk we will present a result which reduces classification of simple transitive 2-representations of a fiat 2-category to classification of simple transitive 2-representations of its certain "much smaller" subquotient 2-categories. The result resembles the reduction of classification of simple modules over a finite semigroup to classification of simple modules over its maximal subgroup. This is a joint work with Marco Mackaay, Volodymyr Mazorchuk and Vanessa Miemietz.