• Title: Asymptotics in finite monoidal categories
  • Authors: Abel Lacabanne, Daniel Tubbenhauer and Pedro Vaz
  • Status: To appear in Proc. Amer. Math. Soc. Last update: Thu, 6 Jul 2023 15:09:44 UTC
  • ArXiv link:
  • 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.