BV-Categories of Spacetime Interventions

Abstract

We use the Chu construction to functorially build BV-categories from duoidal categories, demonstrating that candidate models of BV-logic can be cofreely constructed from a fragment of a model of Guglielmi’s sequencing operator. By using this construction to show that the strong Hyland envelope is a BV-category, we find a way to build a canonical model of spatio-temporal relationships between agents in spacetime from any symmetric monoidal category. The concrete physical interpretation of spacetime events in this model as intervention–context pairs resolves deficiencies in previous attempts to give a general categorical semantics to quantum supermaps.