The proarrow-equipment approach to nondeterministic bicategorical automata

Let $\bbB$ be a bicategory. Recall that automata in the Kleisli category of the powerset monad model nondeterministic automata in $\operatorname{Set}$, and that the presheaf construction on $\operatorname{Cat}$ has a Kleisli bicategory $\operatorname{Prof}$. A generic proarrow equipment for $\bbB$ is intended to provide a bicategorical analogue of this Kleisli construction. The proarrow-equipment conjecture. Nondeterministic bicategorical automata in $\bbB$ might be represented as deterministic bicategorical automata in a generic proarrow equipment for $\bbB$. This is proposed as a direction for future research: the paper argues by analogy with the powerset Kleisli construction, but does not formulate or establish a precise theorem.