10 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 $\mathsf {BaireMeas}$ be the category of Baire measurable spaces, and let $\mathsf {BaireStoch}$ be its associated Markov category of kernels. A Markov functor is understood to…

The finite-first-moment span conjecture. This span would satisfy the conditions of the partial-algebra characterization. However, this is false: the proposed span does not satisfy…

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…

Maybe-monad procedure conjecture. A similar procedure may exist in Kleisli categories of Maybe monads on other Markov categories.

A graded distributive Markov category is a Markov category equipped with the grading and distributive structure described above, and a commutative affine graded relative monad is a…

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…

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…

Conditional-expectation Markov category conjecture. Such a Markov category exists, with conditionals in the sense of the paper's definition, and these conditionals are given by con…