A BV-Category of Spacetime Interventions

TL;DR

This paper introduces a categorical framework for modeling spacetime interventions using BV-categories derived from duoidal categories, providing a new semantic foundation for quantum supermaps and spatio-temporal relationships.

Contribution

It constructs BV-categories functorially from duoidal categories and demonstrates their application to modeling spacetime events and quantum supermaps.

Findings

BV-categories can be built from duoidal categories using the Chu construction.

The strong Hyland envelope is shown to be a BV-category.

A canonical model of spacetime interventions is developed from symmetric monoidal categories.

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 Retor\'e'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.