# Pyramids and their applications

#### Xiaoting Zhang, University of Uppsala. Part of the algebra seminar series.

In this talk, we define the category of pyramids over an additive category. If a strict monoidal structure is enclosed over the additive category, the strictness will be preserved when the monidal structure is lifted to the category of pyramids (avoiding any use of direct sums). The latter is biequivalent to the category of complexes and this biequivalence can be induced onto the corresponding homotopy categories. And a strict monoidal action can be also defined on 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.

After each talk at 4:15pm there will be tea/coffee in the Common Room at level 9 in Maths building. The current seminar organiser is Eleonore Faber.

Xiaoting Zhang, University of Uppsala

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