Double Categorical Approaches to AQFT
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We present a double categorical formulation of Algebraic Quantum Field Theory (AQFT). The construction is expressed as a double functor from the double category of regions of Minkowski spacetime to a double category of von Neumann algebras (vNAs). vNAs provide a natural setting for quantum observables, while their bimodules and intertwiners capture channels and interfaces that go beyond what is visible in ordinary 1-categorical nets. Within this framework, the Haag–Kastler axioms can be phrased in terms of double functoriality and the interchange law, offering a new structural perspective on locality and gluing. We also sketch directions toward incorporating Tomita–Takesaki modular theory for type III vNAs through double functors, and discuss possible connections to categorical models of quantum computation. Slides