Characterization of Contextuality with Semi-Module \v{C}ech Cohomology and its Relation with Cohomology of Effect Algebras

TL;DR

This paper introduces a generalized ;Cech cohomology framework on semi-modules to characterize non-disturbing contextual behaviors, improving upon traditional methods and relating to effect algebra cohomologies.

Contribution

It develops a new cohomology-based approach on semi-modules for contextuality, avoiding false positives and connecting with effect algebra cohomology.

Findings

Generalized ;Cech cohomology characterizes contextual behaviors.

Framework avoids false positives common in previous methods.

Establishes relationships between semi-module cohomology and effect algebra cohomology.

Abstract

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.