Year: 2025
Type: article
Abstract: We present a counterexample showing that Markov categories with conditionals (such as BorelStoch) need not validate a natural scheme of axioms which we call contraction identities.These identities hold in every traced monoidal category, so in particular this shows that BorelStoch cannot be embedded in any traced monoidal category.We remedy this under the additional assumption of atomicity: Atomic Markov categories validate all contraction identities, and furthermore admit a notion of trace defined for non-signalling morphisms.We conclude that atomic Markov categories allow for an intrinsic theory of combs without having to assume an embedding into a compact-closed category.
DOI: 10.4204/eptcs.429.4
Authors: Dario Stein, Márk Széles
Institution: Radboud University Nijmegen
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4414402356