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Room P4.35, Mathematics Building

Volodymyr Mazorchuk, Univ. Uppsala

The endomorphism category of a cell 2-representation

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.

Categorification mini-workshop