A BV-Category of Spacetime Interventions
quant-ph, cs.LO, math.CT
Submitted: 2025-02-26
Updated: 2025-02-26
DOI: 10.1007/s10485-026-09894-8
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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
Terminology
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.
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