Group partition categories

@article{Likeng2021GroupPC,
  title={Group partition categories},
  author={Samuel Nyobe Likeng and Alistair Savage},
  journal={Journal of Combinatorial Algebra},
  year={2021}
}
To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of $\mathcal{P}\mathit{ar}(G)$ into the group Heisenberg category associated to $G$. This embedding intertwines the natural actions of both categories on modules for wreath products of $G$. Finally, we prove… 
2 Citations

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