TL;DR
This paper provides explicit formulas to determine the long-term growth rate of summands in tensor powers within specific finite monoidal categories, enhancing understanding of their asymptotic behavior.
Contribution
It introduces explicit formulas for asymptotic growth in tensor powers of finite monoidal categories with finitely many indecomposables, a novel analytical approach.
Findings
Explicit formulas for growth rates in tensor powers
Applicable to categories with finitely many indecomposables
Advances understanding of asymptotic structures in monoidal categories
Abstract
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.
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