Definition Fibered Conditionals [efr-001F]

Let p: \mathcal {D} \to \mathcal {C} be a Markov fibration. We say it is stochastically complete if, given a Cartesian morphism in the fibration f: X \to Y \in \mathcal {D} \times _\mathcal {C} \mathcal {C}_\mathrm {det}, and a deterministic morphism g: Z \to Y \in \mathcal {D}_\mathrm {det} (recall that \mathcal {D}_\mathrm {det} is still fibred over \mathcal {C}_\mathrm {det}), there is a bijection between the set of morphisms h: p(Z) \to p(X) \in \mathcal {C} so that the triangle

commutes, and the set of morphisms \bar {h}: Z \to X \in \mathcal {D} so that the triangle

commutes, (with the bijection given by applying p).