On quasi-monoidal comonads and their corepresentations

Dingguo Wang; Xiaohui Zhang; Dingguo Wang; Xiaohui Zhang

doi:10.3934/era.2022160

Electronic Research Archive

2022, Volume 30, Issue 8: 3153-3171. doi: 10.3934/era.2022160

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Research article

On quasi-monoidal comonads and their corepresentations

Dingguo Wang ,
Xiaohui Zhang ^,

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received: 20 March 2022 Revised: 12 May 2022 Accepted: 17 May 2022 Published: 17 June 2022

In this paper, we define and study quasi-monoidal comonads on a monoidal category. It generalize the (Hom type) coquasi-bialgebras to a non-braided setting. We investigate their corepresentations and their coquasitriangular structures. We also discuss their gauge equivalence relations.
- quasi-monoidal comonads,
- coquasitriangular structures,
- gauge transformations,
- monoidal categories
Citation: Dingguo Wang, Xiaohui Zhang. On quasi-monoidal comonads and their corepresentations[J]. Electronic Research Archive, 2022, 30(8): 3153-3171. doi: 10.3934/era.2022160

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Abstract

In this paper, we define and study quasi-monoidal comonads on a monoidal category. It generalize the (Hom type) coquasi-bialgebras to a non-braided setting. We investigate their corepresentations and their coquasitriangular structures. We also discuss their gauge equivalence relations.

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