PreprintCC BY 4.0arXiv
A diagrammatic presentation for every pivotal pointed fusion category
Abstract
We provide a generators and relations presentation of pivotal pointed fusion categories, $Vec(G,ω,π)$. Unlike the well-known skeletal model, our presentation is strict and allows multiple isomorphic objects. Our main tool is skein theory, which allows us to apply topological tools to understand the relations of morphisms in the category.
Related
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- Derived category of moduli of pointed curves: II
- Explicit H3 relation in the diagrammatic Hecke category
- Day Convolution and Homotopy Groups on the Pointed Homotopy Category of CW Complexes
- Classifying Grothendieck rings of pivotal fusion categories of rank four
BibTeX
@misc{di2026diagrammatic,
title = {{A diagrammatic presentation for every pivotal pointed fusion category}},
author = {Chumeng Di and Anup Poudel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27295},
eprint = {2609.27295},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27295},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A diagrammatic presentation for every pivotal pointed fusion category
AU - Chumeng Di
AU - Anup Poudel
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27295
UR - https://arxiv.org/abs/2609.27295
AB - We provide a generators and relations presentation of pivotal pointed fusion categories, $Vec(G,ω,π)$. Unlike the well-known skeletal model, our presentation is strict and allows multiple isomorphic objects. Our main tool is skein theory, which allows us to apply topological tools to understand the relations of morphisms in the category.
ER -