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.