• Title: Asymptotics in finite monoidal categories
  • Authors: Abel Lacabanne, Daniel Tubbenhauer and Pedro Vaz
  • Status: Proc. Amer. Math. Soc. Ser. B 10 (2023), 398-412. Last update: Thu, 9 Nov 2023 08:10:44 UTC
  • ArXiv link:
  • ArXiv version = 0.99 published version
  • LaTex Beamer presentation: Slides


We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.

A few extra words

The main theorems of the note give an explicit formula \(a(n)\) to compute the asymptotic growth of summands in tensor products \(b(n)\) for a large class of categories.
For example, for dihedral Soergel bimodules one gets:

The note contains many more examples with explicit formulas.