Pyramids and 2-representations

Volodymyr Mazorchuk, Xiaoting Zhang, Vanessa Miemietz

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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.

Original languageEnglish
Pages (from-to)387–405
Number of pages19
JournalRevista Matemática Iberoamericana
Volume36
Issue number2
Early online date25 Nov 2019
DOIs
Publication statusPublished - 2020

Keywords

  • 2-category
  • 2-representation
  • Finite dimensional algebra
  • Projective bimodule
  • Simple transitive 2-representation

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