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Twisted Post-Hopf Algebras, Twisted Relative Rota-Baxter Operators and Hopf Trusses (2402.16704v4)
Published 26 Feb 2024 in math.RA and math.CT
Abstract: 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.