Room P4.35, Mathematics Building
Fiat 2-categories are 2-analogues of finite dimensional algebras with involutions. Cell 2-representations of fiat 2-categories are most appropriate analogues for simple modules over finite dimensional algebras. In this talk I will try to describe (under some natural assumptions) a 2-analogue of Schur's Lemma which asserts that the endomorphism category of a cell 2-representation is equivalent to the category of vector spaces. This is applicable, for example to the fiat category of Soergel bimodules in type A. This is a report on a joint work with Vanessa Miemietz.