Asymptotics in infinite monoidal categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913002573266944 |
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| author | Lacabanne, Abel Tubbenhauer, Daniel Vaz, Pedro |
| author_facet | Lacabanne, Abel Tubbenhauer, Daniel Vaz, Pedro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics in infinite monoidal categories Lacabanne, Abel Tubbenhauer, Daniel Vaz, Pedro Category Theory Combinatorics Representation Theory Primary: 11N45, 18M05, Secondary: 05C81, 15A18, 20C20 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. |
| title | Asymptotics in infinite monoidal categories |
| topic | Category Theory Combinatorics Representation Theory Primary: 11N45, 18M05, Secondary: 05C81, 15A18, 20C20 |
| url | https://arxiv.org/abs/2404.09513 |