Twisted Post-Hopf Algebras, Twisted Relative Rota-Baxter Operators and Hopf Trusses
Copyright policy )Twisted Post-Hopf Algebras, Twisted Relative Rota-Baxter Operators and Hopf Trusses
The present article is devoted to studying the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras, introduced by Wang (2023), and weak twisted relative Rota-Baxter operators. The latter objects are a generalisation of the relative Rota-Baxter operators defined by Li-Sheng-Tang (2024), where the Rota-Baxter condition is modified through a cocycle. Under certain conditions, this work shows that the three aforementioned categories are equivalent.
Hopf algebras and their applications, braided monoidal category, weak twisted post-Hopf algebra, 18M05, 16T05, 17B38, Mathematics - Category Theory, Mathematics - Rings and Algebras, Weak twisted relative Rota-Baxter operator, Hopf algebra, Rings and Algebras (math.RA), weak twisted relative Rota-Baxter operator, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Category Theory (math.CT), 1201.05 Campos, Anillos, Álgebras, Braided monoidal category, Yang-Baxter equations and Rota-Baxter operators, Weak twisted post-Hopf algebra, Hopf truss
Hopf algebras and their applications, braided monoidal category, weak twisted post-Hopf algebra, 18M05, 16T05, 17B38, Mathematics - Category Theory, Mathematics - Rings and Algebras, Weak twisted relative Rota-Baxter operator, Hopf algebra, Rings and Algebras (math.RA), weak twisted relative Rota-Baxter operator, FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Category Theory (math.CT), 1201.05 Campos, Anillos, Álgebras, Braided monoidal category, Yang-Baxter equations and Rota-Baxter operators, Weak twisted post-Hopf algebra, Hopf truss
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