Category forms of Local-Causality and Non-Signalling and their duals

Abstract

Two fundamental (meta)physical principles – NS (Non-Signalling condition which states the impossibility to communicate by means of physical correlations) and LC (the principle of Local Causality which isolates classical correlations from those responsible for non-locality) are considered in the framework of category theory. The original form of these principles operates with properties of common probability distributions for outcomes of measurements implemented in two space-time regions. The suggested category form consists of some assertions about special commutative diagrams. To any common probability distribution in the matter of discourse, an arrow (morphism) in these diagrams is associated. In fact, LC turns into the condition of the arrow being able to factor through a definite standard arrow. NS looks like uniqueness of an arrow which makes commutative a special diagram incorporating the considered arrow associated to the distribution. By means of these diagrams dual forms of NS and LC are suggested.