Higher Structures, Vol. 9, No. 2, pp. 168-197, 2025
Asymptotics in infinite monoidal categories
Abel Lacabanne, Daniel Tubbenhauer, Pedro Vaz
Received April 15th 2024. Published online November 25th 2025.
Abstract: We discuss formulas for the asymptotic growth rate of the number of summands in tensor powers in certain (finite or infinite) monoidal categories. Our focus is on monoidal categories with infinitely many indecomposable objects, with our main tools being generalized Perron-Frobenius theory alongside techniques from random walks.
Keywords: Monoidal categories; growth problems; random walks; Perron-Frobenius theory.
