Twisted post-Hopf algebras, twisted relative Rota-Baxter operators and Hopf trusses

The present article is devoted to study the categorical relationships between the categories of Hopf trusses, weak twisted post-Hopf algebras and weak twisted relative Rota-Baxter operators. The latter objects are a generalisation of relative Rota-Baxter operators where the Rota-Baxter condition is modified through a cocycle. Under certain conditions, this work shows that the three aforementioned categories are equivalent.