Induction and restriction in 2-representation theory (Vanessa Miemietz)

Orateur : Vanessa Miemietz

Lieu : salle des Séminaires M3

Résumé :

For a finite-dimensional algebra A with a subalgebra B, there is the well-known adjunction between induction and restriction (Ind^A_B , Res^A_B) where Ind^A_B = A\otimes_B-. For 2-representations of 2-categories, an analogue of restriction is straightforward, but a lack of relative tensor product means we need to define induction differently in order to obtain an analogous 2-adjunction between induction and restriction (for finitary 2-representations of fiat 2-categories). I will explain the basics of 2-representation theory and the necessary ingredients to state this 2-adjunction.