7 problems

Causal-channel conjecture. The difference between the authors' causal-trace axioms and the axioms of a partial trace is similar to the difference addressed by Houghton–Larsen's con…

Let $\vV$-theories be the enriched theories considered in the paper. A $\vV$-theory is cartesian when it is equipped with natural copy and discard structure. Comparison conjecture.…

Let $\mathcal M$ be the monad on probability sheaves defined by … Let $\operatorname{Kl}(\mathcal M)$ denote its Kleisli category, and let $\mathbb{{C}}$ be the underlying Markov c…

Free Markov category conjecture. Free Markov categories are atomic and have supports, but do not have conditionals.

Let $\mathsf{C}$ be a Markov category with supports, and let $p$ and $q$ be morphisms in $\mathsf{C}$. Write $S_f$ for the support object of a morphism $f$. Support tensor-product…

Positivity correspondence conjecture. The monad $T$ is positive if and only if its Kleisli category $\mathrm{Kl}_T$ is positive.

Let $\Sigma$ be a monoidal signature, and let $\mathsf{FreeMarkov}_\Sigma$ denote the free Markov category generated by $\Sigma$. A box has an output when its output list is nonemp…