  In this paper we introduce the notion of generalized invertible 1-cocycle in
a strict braided monoidal category C, and we prove that the category of Hopf
trusses is equivalent to the category of generalized invertible 1-cocycles. On
the other hand, we also introduce the notions of module for a Hopf truss and
for a generalized invertible 1-cocycle. We prove some functorial results
involving these categories of modules and we show that the category of modules
associated to a generalized invertible 1-cocycle is equivalent to a category of
modules associated to a suitable Hopf truss. Finally, assuming that in C we
have equalizers, we introduce the notion of Hopf-module in the Hopf truss
setting and we obtain the Fundamental Theorem of Hopf modules associated to a
Hopf truss.
