  I present a generalized notion of obstruction in \v{C}ech cohomology on
semi-modules, which allows one to characterize non-disturbing contextual
behaviors with any semi-field. This framework generalizes the usual \v{C}ech
cohomology used in the sheaf approach to contextuality, avoiding false
positives. I revise a similar work done in the framework of effect algebras
with cyclic and order cohomologies and explore the relationship with the one
presented here.
