Definition Stochastic Module Fibration [efr-OEFJ]

Let \mathcal {C} be a pullback-positive Markov category. The adjunction \overline {(-)} \dashv (-)|_\mathrm {det} induces a monad on \mathsf {Fib}(\mathcal {C}_\mathrm {det}). A module for this monad is called a stochastic module over \mathcal {C} (or, to distinguish it from the copresheaves of Definition [efr-Y926], a stochastic module fibration). The category of stochastic module fibrations is denoted \mathsf {SFib}(\mathcal {C})