Matematiska institutionen

Algebra- och geometriseminarium: Pyramids, strict monoidal actions and 2-representations

  • Datum: 2017-10-10 kl 15:15
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Xiaoting Zhang (Uppsala)
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium

Abstract:

By the construction of taking the total complex, the monoidal structure of the category of complexes over an additive strict monoidal category will lose the strictness as there is no strict distributivity with respect to the tensor product and direct sum. In this talk, we introduce the category of pyramids whose tensor structure is defined avoiding direct sums and preserves strictness. It is biequivalent to the category of complexes and the biequivalence can be induced onto the corresponding homotopy categories. Similarly, a strict monoidal action of an additive strict monoidal category can be also lifted to a strict one of the (homotopy) category of pyramids.

As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.

This is joint work with Volodymyr Mazorchuk and Vanessa Miemietz.