JournalsrmiVol. 36, No. 2pp. 387–405

Pyramids and 2-representations

  • Volodymyr Mazorchuk

    Uppsala Universitet, Sweden
  • Vanessa Miemietz

    University of East Anglia, Norwich, UK
  • Xiaoting Zhang

    Uppsala Universitet, Sweden
Pyramids and 2-representations cover

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Abstract

We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. 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.

Cite this article

Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang, Pyramids and 2-representations. Rev. Mat. Iberoam. 36 (2019), no. 2, pp. 387–405

DOI 10.4171/RMI/1133