Categorical supermaps on any generalised theory with channel-state duality are exactly CJ-supermaps, recovering classical, quantum, and NSWSE-Boxworld supermaps.
Acategoricalsemanticsforcausalstructure.Logical Methods in Computer Science, 15
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Constructs the exponential A^B and proves existence of tensor A ⊗ B on contextual categories such that bimorphisms correspond to morphisms from the tensor, extending to a closed symmetric monoidal structure on Cont.
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Supermaps on generalised theories
Categorical supermaps on any generalised theory with channel-state duality are exactly CJ-supermaps, recovering classical, quantum, and NSWSE-Boxworld supermaps.
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A monoidal category of dependently sorted algebraic theories II: categorical aspects
Constructs the exponential A^B and proves existence of tensor A ⊗ B on contextual categories such that bimorphisms correspond to morphisms from the tensor, extending to a closed symmetric monoidal structure on Cont.