Example [efr-C5RE]

\mathsf {BorelStoch}^\to , as we have noted, is a Markov prefibration, and hence induces a stochastic module structure on \mathsf {BorelStoch}^\to |_\mathrm {det}. This structure does not present a Markov fibration. To see this, note that in that case its fiberwise opposite would also present a Markov fibration. Then this fibration, \mathsf {SLens}(\mathsf {BorelStoch}^\to |_\mathrm {det}), would be a prefibration whose deterministic part was \mathsf {BorelStoch}^\to |_\mathrm {det}^\mathrm {fop}. But Example [efr-8B5X] shows that this is impossible.