Higher-Order Quantum Objects are Strong Profunctors

• URL: http://arxiv.org/abs/2603.11221v1
• Date: Wed, 11 Mar 2026 18:35:59 GMT
• Title: Higher-Order Quantum Objects are Strong Profunctors
• Abstract summary: We construct a functor F : Caus(C) -> StProf(C1) from higher-order causal categories to the category of strong profunctors over first-order causal processes.<n>We conclude that insofar as compositional constraints can be used to express causality constraints, the profunctorial approach generalises higher-order quantum theory to a construction over general symmetric monoidal categories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coincide. More precisely, we construct a functor F : Caus(C) -> StProf(C1) from higher-order causal categories to the category of strong profunctors over first-order causal processes that is lax-lax duoidal, full, faithful, and strongly closed whenever C is additive. When C = CP this embedding is furthermore strong on the sequencer for duoidal categories, expressing the possibility to interpret one-way signalling (but not general non-signalling) constraints in terms of the coend calculus for profunctors. We conclude that insofar as compositional constraints can be used to express causality constraints, the profunctorial approach generalises higher-order quantum theory to a construction over general symmetric monoidal categories.

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