  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.
