A BV-Category of Spacetime Interventions

2025/02/26 by Hefford, James, Wilson, Matt · 1 citation
#Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Logic in Computer Science (cs.LO) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2502.19022

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 Retoré'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.

Cited by

• On Decision-Making Agents and Higher-Order Causal Processes

Related

• A New Approach to Quantising Space-Time: I. Quantising on a General Category
• Categorical Semantics for Time Travel
• Higher-order causal theories are models of BV-logic
• On the equivalence of AQFTs and prefactorization algebras
• Model Categories and Quantum Gravity