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Crossed Burnside rings for groupoids
Abstract
In this paper, we extend the classical theory of crossed G-sets and the crossed Burnside ring from a finite group G to a finite groupoid π’. We introduce a natural monoidal structure on the category of crossed π’-sets over a π’-monoid and construct the corresponding crossed Burnside ring of a π’-monoid. Finally, we prove a decomposition theorem that expresses the crossed Burnside ring of a groupoid as a product of crossed Burnside rings of groups.
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BibTeX
@misc{shiizuka2026crossed,
title = {{Crossed Burnside rings for groupoids}},
author = {Keitaro Shiizuka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.03401},
eprint = {2605.03401},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03401},
}
RIS
TY - UNPB
TI - Crossed Burnside rings for groupoids
AU - Keitaro Shiizuka
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2605.03401
UR - https://arxiv.org/abs/2605.03401
AB - In this paper, we extend the classical theory of crossed G-sets and the crossed Burnside ring from a finite group G to a finite groupoid π’. We introduce a natural monoidal structure on the category of crossed π’-sets over a π’-monoid and construct the corresponding crossed Burnside ring of a π’-monoid. Finally, we prove a decomposition theorem that expresses the crossed Burnside ring of a groupoid as a product of crossed Burnside rings of groups.
ER -